931:
993:
66:
2425:
906:
1820:
2323:
1808:
918:
2172:
2947:
the poor to the rich results in a bigger increase in the utility of the rich than the decrease in the utility of the poor, the society is expected to accept such a transfer, because the total utility of the society has increased as a whole. Alternatively, society's welfare can also be measured under this function by taking the average of individual incomes:
2213:
2268:
2946:
individuals in society. In this case, maximizing the social welfare means maximizing the total income of the people in the society, without regard to how incomes are distributed in society. It does not distinguish between an income transfer from rich to poor and vice versa. If an income transfer from
2640:
of utility for everyone in the society from ethically lowest on up (with ties permitted), that is, it makes interpersonal comparisons of utility. Welfare maximization then consists of maximizing the welfare function subject to the possibility function as a constraint. The same welfare maximization
2026:
Every social ordering can be made into a choice function by considering only the highest-ranked outcome. Less obviously, though, every social choice function is also an ordering function. Deleting the best outcome, then finding the new winner, results in a runner-up who is assigned second place.
3117:
These two social welfare functions express very different views about how a society would need to be organised in order to maximize welfare, with the first emphasizing total incomes and the second emphasizing the needs of the worst-off. The max-min welfare function can be seen as reflecting an
2736:. This axiom says that changing the value of one outcome should not affect choices that do not involve this outcome. For example, if a customer buys apples because he prefers them to blueberries, telling them that cherries are on sale should not make them buy blueberries instead of apples.
2635:
locus of utility combinations imposed by the restraints and allowed by Pareto efficiency. At a given point on the possibility function, if the utility of all but one person is determined, the remaining person's utility is determined. The welfare function ranks different hypothetical
3452:
may belong, which is randomly picked from the sum of all unequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to. The inverse value of that function will be larger than the average per capita income.
2592:
dimension. As
Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.
3736:
By
Harsanyi's theorem, any non-utilitarian social choice function will be incoherent; in other words, it will agree to some bets that are unanimously opposed by every member of society. However, it is still possible to establish properties of such functions.
2630:
the set of utility functions for everyone in the society. Each can (and commonly does) incorporate Pareto efficiency. The possibility function also depends on technology and resource restraints. It is written in implicit form, reflecting the
1901:
that ranks a set of social states by their desirability. A social welfare function may yield several possible outcomes; each person's preferences are combined in some way to determine which outcome is considered better by society as a whole.
2693:
demonstrated the problems with such an approach, though he would not immediately realize this. Along earlier lines, Arrow's version of a social welfare function, also called a 'constitution', maps a set of individual orderings
2568:, which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a
3443:
3347:
3744:: the relation between two utility profiles does not change if both of them are multiplied by the same constant. For example, the utility function should not depend on whether we measure incomes in cents or dollars.
3025:
2778:), and returns as output a numeric representation of the collective welfare. The underlying assumption is that individuals utilities can be put on a common scale and compared. Examples of such measures include
1909:
as a way to identify socially-optimal decisions, giving a procedure to rigorously define which of two outcomes should be considered more desirable for society as a whole (e.g. to compare two different possible
3551:
prefers (2, 2, 4) to (1, 3, 4), it also prefers (2, 2, 9) to (1, 3, 9); the utility of agent 3 should not affect the comparison between two utility profiles of agents 1 and 2. This property can also be called
2662:
The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve
3666:
1984:(non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting, making any such ordinal decision procedure a
3195:
3356:, who randomly is selected from a population with an unequal distribution of incomes. This welfare function marks the income, which a randomly selected person is most likely to have. Similar to the
2678:
Two-person welfare maximization at the tangency of the highest
Welfare function curve on the Possibility function is analogous to tangency of the highest indifference curve on the budget constraint.
3476:
on utility profiles—it can tell us, given any two utility profiles, if they are indifferent or one of them is better than the other. A reasonable preference ordering should satisfy several axioms:
4284:
3109:
2548:
3811:
2547:
measurable, and it was commonly inferred that redistributing income from a rich person to a poor person tends to increase total utility (however measured) in the society. But Lionel
Robbins (
2615:
As
Samuelson (1983, p. xxii) notes, Bergson clarified how production and consumption efficiency conditions are distinct from the interpersonal ethical values of the social welfare function.
2854:
2108:
Under instant-runoff voting, Top is the winner. Center is eliminated in the first round, and their second-preferences are evenly split between Top and Bottom, allowing Top to win.
3846:
3945:
2492:
with the intention "to state in precise form the value judgments required for the derivation of the conditions of maximum economic welfare." The function was real-valued and
959:
2231:
4441:
3912:
3879:
3979:
3230:
2904:
3722:
3250:
2944:
2924:
2877:
2496:. It was specified to describe the society as a whole. Arguments of the function included the quantities of different commodities produced and consumed and of
4891:
4659:
3688:
3448:
Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which a
650:
6136:
6092:
4218:
3684:
2751:
2718:
1850:
1782:
2572:) as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a
3114:
Here maximizing societal welfare would mean maximizing the income of the poorest person in society without regard for the income of other individuals.
1980:
is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a
2551:, ch. VI) argued that how or how much utilities, as mental events, change relative to each other is not measurable by any empirical test, making them
4787:
4639:
2340:
2286:
2185:
682:
544:
539:
4886:
4664:
2733:
952:
645:
3366:
3270:
4188:
2648:
4649:
4434:
2698:) for everyone in society to a social ordering, which ranks alternative social states (such as which of several candidates should be elected).
327:
2562:
Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define
4094:
3489:
should strictly prefer the second profile. For example, it should prefer the profile (1, 4, 4, 5) to (1, 2, 4, 5). Such a change is called a
851:
5013:
102:
2953:
5140:
5063:
4696:
4165:
2690:
2540:
2387:
2046:
election between Top, Center, and Bottom. Top has the most first-preference votes; Bottom has the second-most; and Center (positioned
945:
4427:
4379:
4312:
4250:
4207:
4173:
4142:
2471:
2406:
2359:
2304:
2249:
2199:
5031:
3573:
2111:
To find the second-place finisher, we find the winner if Top had not run. In this case, the election is between Center and Bottom.
846:
4881:
4827:
4303:
3996:
2722:
2597:
1977:
836:
586:
557:
497:
4679:
6171:
5008:
4036:
2366:
1843:
568:
93:
3134:
5574:
4807:
3122:
on the part of society as a whole, since it is concerned only with the worst conditions that a member of society could face.
2344:
631:
2278:
2608:
a complete and transitive ranking (an ethically "better", "worse", or "indifferent" ranking) of all social alternatives and
2018:
function maps each candidate to a number representing their quality. For example, the standard social scoring function for
6166:
5755:
5544:
5534:
5227:
3560:. It allows us to treat allocation problems in a local way, and separate them from the allocation in the rest of society.
2155:
1443:
1181:
273:
258:
243:
3352:
The value yielded by this function has a concrete meaning. There are several possible incomes which could be earned by a
3034:) measures the social welfare of society on the basis of the welfare of the least well-off individual member of society:
2373:
5694:
5667:
4850:
4835:
4654:
4001:
3725:
2743:
2510:
The marginal "dis-welfare" of each "dollar's worth" of labor is equal for each commodity produced of each labor supplier
2446:
2191:
889:
509:
432:
353:
3040:
2437:
6121:
6102:
5679:
5524:
5490:
5475:
5454:
5449:
4901:
4624:
4614:
4475:
3760:
1792:
1012:
1002:
321:
303:
144:
3957:
874:
2588:
dimension of a particular social welfare function with distribution of commodities among individuals characterizing
2513:
The marginal "dollar" cost of each unit of resources is equal to the marginal value productivity for each commodity.
2355:
6161:
6096:
5672:
5362:
5352:
4866:
4557:
4340:
2019:
1836:
1786:
1316:
1306:
765:
748:
715:
695:
479:
467:
437:
238:
196:
129:
2728:
Arrow's theorem shows that it is impossible for an ordinal social welfare function to satisfy a standard axiom of
2584:
but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize
2333:
573:
5242:
4916:
4871:
4817:
4729:
3497:
1196:
621:
614:
98:
6126:
6072:
5815:
5770:
5609:
5480:
5357:
4906:
4792:
4750:
4669:
4594:
4530:
4488:
4006:
3882:
2695:
2004:
function selects a single best outcome (a single candidate who wins, or multiple if there happens to be a tie).
1765:
1503:
1458:
1311:
1080:
1024:
675:
603:
592:
455:
442:
425:
402:
380:
343:
333:
5830:
4525:
4389:
3740:
Instead of imposing rational behavior on the social utility function, we can impose a weaker criterion called
1518:
2647:
For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of
5780:
5614:
5604:
5594:
5584:
5322:
5312:
5272:
5262:
5135:
5056:
4931:
4921:
4896:
4712:
4589:
3257:
2805:
2493:
1468:
1276:
1266:
1226:
1216:
1123:
1046:
801:
655:
338:
1933:
utility functions onto a single output, in a way that accounts for the judgments of everyone in a society.
5950:
5795:
5655:
5598:
5554:
5517:
5267:
5207:
5182:
5152:
5125:
4972:
4911:
4774:
4717:
3480:
2627:
1981:
1898:
1638:
1483:
1221:
1161:
1118:
1065:
830:
710:
640:
447:
5765:
1453:
6082:
5740:
5725:
5699:
5638:
5317:
5257:
5237:
5232:
4876:
4797:
4562:
2497:
2043:
1772:
1428:
1413:
1271:
1211:
1191:
1186:
738:
578:
462:
268:
247:
179:
157:
3822:
3260:'s Indexes, which is an entropy measure. Due to the relation between Atkinsons entropy measure and the
2788:
The form of the social welfare function is intended to express a statement of objectives of a society.
2528:, the hypothesization of which may merely conceal value judgments, and purely subjective ones at that.
930:
796:
4348:
3924:
3510:. This axiom formalizes the idea that every person should be treated equally in society. For example,
6131:
5835:
5579:
5549:
5502:
5465:
5391:
5342:
5307:
5247:
5212:
5147:
5130:
4946:
4515:
4330:
4317:
_____, 1977. "Reaffirming the
Existence of 'Reasonable' Bergson–Samuelson Social Welfare Functions,"
4041:
3514:
should be indifferent between (1, 4, 4, 5) and (5, 4, 4, 1), because the only difference is whether
3119:
2543:
as implying interpersonally comparable utility. Irrespective of such comparability, income or wealth
2380:
2031:
1868:
1523:
1345:
1296:
1261:
1201:
1166:
1070:
1060:
1007:
869:
856:
824:
88:
6061:
5870:
5730:
5689:
5589:
5569:
5529:
5485:
5470:
5426:
5367:
5292:
5282:
5252:
5175:
4926:
4520:
4026:
3991:
3462:
1911:
1749:
1558:
1418:
1380:
1321:
1246:
1236:
1206:
1133:
1041:
775:
609:
262:
6116:
6087:
6045:
5850:
5559:
5539:
5507:
5421:
5416:
5396:
5347:
5287:
5277:
5222:
5217:
5049:
4967:
4577:
4226:
3752:
3030:
In contrast, the max-min or
Rawlsian social welfare function (based on the philosophical work of
2774:
is a function that takes as input numeric representations of individual utilities (also known as
2611:
one set out of an infinity of welfare indices and cardinal indicators to characterize the belief.
2047:
1777:
1733:
1538:
1375:
1370:
1350:
1301:
1241:
1231:
1176:
1171:
1143:
1138:
1108:
976:
935:
806:
417:
201:
4535:
884:
2600:, p. 221) himself stressed the flexibility of the social welfare function to characterize
2580:(2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as
5980:
5955:
5905:
5865:
5745:
5633:
5436:
5372:
5337:
5327:
5197:
4936:
4845:
4802:
4722:
4644:
4567:
4552:
4510:
4375:
4308:
4298:
4273:
4246:
4238:
4234:
4203:
4169:
4138:
4090:
4046:
4021:
4016:
3490:
2755:
2564:
2518:
1864:
1668:
1643:
1593:
1553:
1433:
1390:
1326:
1291:
1281:
1113:
1075:
1031:
841:
811:
733:
670:
504:
231:
206:
189:
57:
31:
4393:
3891:
3858:
2799:
social welfare function measures social welfare as the total or sum of individual utilities:
6030:
5975:
5960:
5945:
5930:
5910:
5860:
5840:
5820:
5775:
5382:
5332:
5302:
5297:
5187:
5113:
4977:
4609:
4465:
4450:
4213:
4011:
3692:
2775:
2759:
2710:
2525:
2507:
The marginal "dollar's worth" of welfare is equal for each individual and for each commodity
1966:
1956:
1718:
1663:
1648:
1633:
1618:
1598:
1548:
1528:
1508:
1463:
1336:
1286:
1256:
1251:
922:
879:
770:
758:
472:
348:
174:
168:
150:
139:
134:
122:
83:
45:
3964:
3203:
2882:
992:
6141:
6035:
6000:
5965:
5900:
5825:
5810:
5704:
5660:
5497:
5431:
5406:
5401:
5377:
5108:
5093:
5025:
4941:
4782:
4760:
4572:
4493:
4483:
4461:
4398:
4031:
3698:
2779:
2729:
2714:
2652:
1950:
1940:
1926:
1812:
1723:
1688:
1653:
1588:
1513:
1498:
1385:
1360:
1355:
1331:
1103:
1098:
910:
743:
598:
563:
484:
395:
298:
221:
163:
41:
4276:, 1957, "Theoretical Welfare Economics", 1957, Cambridge, UK: Cambridge University Press.
4111:
4337:
Economic
Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson
2424:
2030:
Because of this close relationship, the three kinds of functions are often conflated by
65:
6055:
6040:
6005:
5990:
5970:
5940:
5790:
5760:
5411:
5120:
5088:
4840:
4545:
4505:
4279:
4065:
3547:
should be independent of individuals whose utilities have not changed. For example, if
3235:
2929:
2909:
2862:
2702:
2577:
2536:
2532:
1743:
1728:
1693:
1678:
1658:
1628:
1478:
1448:
1365:
1055:
1051:
780:
720:
705:
516:
385:
360:
211:
17:
3485:: if the utility of one individual increases, while all other utilities remain equal,
905:
6155:
6020:
6010:
5985:
5925:
5920:
5915:
5895:
5885:
5855:
5845:
5750:
5650:
5623:
5387:
4584:
4178:
4160:
2739:
2686:
2552:
2485:
1946:
1708:
1698:
1673:
1613:
1608:
1603:
1583:
1573:
1543:
1533:
1438:
1341:
789:
489:
277:
115:
78:
53:
4371:
4073:
6050:
5995:
5890:
5880:
5875:
5800:
5645:
5170:
5098:
4599:
4540:
3724:
must be equal to the utility functions of each individual. This result is known as
3264:, Foster's welfare function also can be computed directly using the Theil-L Index.
3200:
The average per capita income of a measured group (e.g. nation) is multiplied with
2785:
For the purposes of this section, income is adopted as the measurement of utility.
1962:
1824:
1738:
1683:
1578:
1568:
1563:
1488:
1036:
529:
293:
286:
216:
4072:, ch. 3, "Collective Rationality." p. 33, and ch. 3*, "Social Welfare Functions."
3563:
Every preference relation with properties 1–4 can be represented as by a function
1925:
The notion of social utility is analogous to the notion of a utility function in
6025:
6015:
5805:
5684:
5628:
5103:
4982:
4745:
4684:
4604:
4500:
4353:
4264:
4195:
3915:
3503:
3473:
3261:
3125:
2792:
2747:
2706:
2556:
2322:
1985:
1713:
1703:
1493:
1128:
407:
365:
308:
253:
30:
For a discussion of the same concept in the context of voting and politics, see
3256:, a relative inequality measure. James E. Foster (1996) proposed to use one of
5935:
5735:
5512:
4755:
4691:
3534:
3253:
3031:
2796:
1623:
1423:
2555:. Robbins therefore rejected such as incompatible with his own philosophical
2158:: despite being eliminated first, Center is the runner-up in this election.)
1996:
Some authors maintain a distinction between three closely-related concepts:
1929:. However, a social welfare function is different in that it is a mapping of
5785:
5715:
5162:
5080:
5072:
4992:
4987:
4401:(1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria,"
2503:
Necessary general conditions are that at the maximum value of the function:
2154:(Note that the finishing order is not the same as the elimination order for
1915:
1906:
1473:
1404:
984:
375:
370:
3438:{\displaystyle W_{\mathrm {Theil-T} }={\overline {Y}}\mathrm {e} ^{-T_{T}}}
3342:{\displaystyle W_{\mathrm {Theil-L} }={\overline {Y}}\mathrm {e} ^{-T_{L}}}
1807:
917:
5564:
4812:
1919:
626:
2521:
had described a standard of economic efficiency despite dispensing with
4674:
4406:
4361:
2347: in this section. Unsourced material may be challenged and removed.
412:
4112:"From social choice functions to dictatorial social welfare functions"
1936:
There are two different notions of social welfare used by economists:
4962:
4335:
_____, 1981. "Bergsonian
Welfare Economics", in S. Rosefielde (ed.),
4245:(2nd ed.), Basingstoke, Hampshire New York: Palgrave Macmillan,
3357:
2721:
behavior at the social level impossible. This result is now known as
27:
Function that ranks states of society according to their desirability
4419:
4356:(1963). "Distribution, Transitivity and Little's Welfare Criteria,"
4322:
3020:{\displaystyle W={\frac {1}{n}}\sum _{i=1}^{n}Y_{i}={\overline {Y}}}
2659:
as to two commodities consumed, there are the following parallels:
4181:(Burk),"A Reformulation of Certain Aspects of Welfare Economics,"
3506:
the values in the utility profile should not change the output of
3360:, this income will be smaller than the average per capita income.
3747:
If the preference relation has properties 1–5, then the function
2576:
individualistic sense to derive Pareto efficiency (optimality).
5045:
4423:
4291:
____, 1938, "Interpersonal
Comparisons of Utility: A Comment,"
2618:
Samuelson further sharpened that distinction by specifying the
2027:
Repeating this process gives a full ranking of all candidates.
3687:, or equivalently that social choice behaves according to the
2675:
The Possibility function is analogous to the budget constraint
2418:
2316:
2261:
2206:
2165:
3661:{\displaystyle W(u_{1},\dots ,u_{n})=\sum _{i=1}^{n}w(u_{i})}
5041:
2669:
The Welfare function is analogous to the indifference-curve
64:
4285:
An Essay on the Nature and Significance of Economic Science
2531:
Earlier neoclassical welfare theory, heir to the classical
2604:
one ethical belief, Pareto-bound or not, consistent with:
2500:
used in producing different commodities, including labor.
2022:
is the total number of voters who rank a candidate first.
3190:{\displaystyle W_{\mathrm {Gini} }={\overline {Y}}(1-G)}
2442:
2227:
3967:
3927:
3894:
3861:
3825:
3763:
3701:
3691:—implies that the social choice function must be the
3683:
Introducing one additional axiom—the nonexistence of
3576:
3369:
3273:
3238:
3206:
3137:
3043:
2956:
2932:
2912:
2885:
2865:
2808:
4345:
The Collected Scientific Papers of Paul A. Samuelson
4327:
The Collected Scientific Papers of Paul A. Samuelson
4307:, pp. xxi–xxiv & ch. VIII, "Welfare Economics,"
2709:, dropping the requirement of real-valued (and thus
6071:
5713:
5447:
5196:
5161:
5079:
5001:
4955:
4859:
4826:
4773:
4738:
4705:
4632:
4623:
4474:
2222:
may be too technical for most readers to understand
4343:, Cambridge, pp. 223–66. Reprinted in (1986)
4191:in Paretian welfare economics from the New School.
3973:
3939:
3906:
3873:
3840:
3805:
3716:
3660:
3437:
3341:
3244:
3224:
3189:
3103:
3019:
2938:
2918:
2898:
2871:
2848:
2011:function lists the candidates, from best to worst.
3918:welfare function—maximizing the sum of utilities.
3104:{\displaystyle W=\min(Y_{1},Y_{2},\cdots ,Y_{n})}
1918:governments to choose between several options in
3806:{\displaystyle {\frac {c^{1-\eta }-1}{1-\eta }}}
3050:
2750:, the unique social welfare function satisfying
2701:Arrow found that contrary to the assertions of
2281:for grammar, style, cohesion, tone, or spelling
3961:(that inequality is not a positive good) then
5057:
4435:
4216:, 1987, “interpersonal utility comparisons,"
1844:
953:
8:
4892:Independence of Smith-dominated alternatives
4089:. New York: PALGRAVE MACMILLAN. p. 67.
2746:that if societies must make decisions under
2641:conditions emerge as in Bergson's analysis.
4414:The New Palgrave: A Dictionary of Economics
4219:The New Palgrave: A Dictionary of Economics
2200:Learn how and when to remove these messages
5064:
5050:
5042:
4629:
4442:
4428:
4420:
4189:Bergson–Samuelson social welfare functions
3529:and the set of profiles weakly worse than
2649:Bergson–Samuelson social welfare functions
1851:
1837:
971:
960:
946:
36:
3966:
3926:
3893:
3860:
3824:
3771:
3764:
3762:
3700:
3649:
3633:
3622:
3606:
3587:
3575:
3525:, the set of profiles weakly better than
3427:
3419:
3414:
3403:
3375:
3374:
3368:
3331:
3323:
3318:
3307:
3279:
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3205:
3162:
3143:
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3073:
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3007:
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2988:
2977:
2963:
2955:
2931:
2911:
2890:
2884:
2864:
2840:
2830:
2819:
2807:
2472:Learn how and when to remove this message
2407:Learn how and when to remove this message
2305:Learn how and when to remove this message
2250:Learn how and when to remove this message
2234:, without removing the technical details.
1973:better one choice is compared to another.
4412:_____, 1987, “social welfare function,"
4243:The new Palgrave dictionary of economics
2113:
2052:
4887:Independence of irrelevant alternatives
4665:Sequential proportional approval voting
4137:. Cambridge, Massachusetts: MIT Press.
4058:
3981:in the above family must be at most 1.
3815:This family has some familiar members:
2734:independence of irrelevant alternatives
1905:Social choice functions are studied by
983:
52:
2849:{\displaystyle W=\sum _{i=1}^{n}Y_{i}}
1922:, based on the preferences of voters.
3885:—maximizing the product of utilities.
3675:is a continuous increasing function.
3128:proposed a welfare function in 1973:
2626:(1947, pp. 243–49). Each has as
2232:make it understandable to non-experts
2050:) has the fewest first preferences.
1969:information, with agents stating how
1965:) functions additionally incorporate
7:
4369:Collective Choice and Social Welfare
4135:Fair Division and Collective Welfare
4070:Collective Choice and Social Welfare
2345:adding citations to reliable sources
5141:Agent-based computational economics
4697:Indirect single transferable voting
4374:, ch. 3, "Collective Rationality."
4166:Social Choice and Individual Values
3542:Independence of unconcerned agents:
2541:law of diminishing marginal utility
3934:
3835:
3415:
3394:
3388:
3385:
3382:
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3376:
3319:
3298:
3292:
3289:
3286:
3283:
3280:
3153:
3150:
3147:
3144:
2742:later strengthened this result by
25:
4229:(2008), "social welfare function
3841:{\displaystyle \eta \to -\infty }
2643:
2436:to comply with Knowledge (XXG)'s
2181:This section has multiple issues.
5599:neoclassical–Keynesian synthesis
4304:Foundations of Economic Analysis
4202:, expanded edition with annexe,
3940:{\displaystyle \eta \to \infty }
2772:cardinal social welfare function
2423:
2321:
2266:
2211:
2170:
1818:
1806:
991:
929:
916:
904:
852:McKelvey–Schofield chaos theorem
498:Semi-proportional representation
130:First preference plurality (FPP)
4386:Choice, Welfare and Measurement
4037:Production-possibility frontier
2332:needs additional citations for
2189:or discuss these issues on the
1093:Concepts, theory and techniques
4808:Mixed ballot transferable vote
4392:and scroll to chapter-preview
4185:, 52(2), February 1938, 310–34
4183:Quarterly Journal of Economics
3931:
3829:
3726:Harsanyi's utilitarian theorem
3711:
3705:
3695:, i.e. the weighting function
3655:
3642:
3612:
3580:
3219:
3207:
3184:
3172:
3098:
3053:
2156:sequential elimination methods
890:Harsanyi's utilitarian theorem
847:Moulin's impossibility theorem
812:Conflicting majorities paradox
1:
5535:Critique of political economy
3997:Arrow's impossibility theorem
2723:Arrow's impossibility theorem
1978:Arrow's impossibility theorem
716:Frustrated majorities paradox
5009:Comparison of voting systems
4851:Satisfaction approval voting
4836:Single non-transferable vote
4655:Proportional approval voting
4002:Community indifference curve
3742:independence of common scale
3567:which is a sum of the form:
3457:Axioms of cardinal welfarism
3408:
3312:
3167:
3012:
2906:is the income of individual
885:Condorcet dominance theorems
825:Social and collective choice
4615:Graduated majority judgment
4301:, 1947, Enlarged ed. 1983,
4085:Tresch, Richard W. (2008).
1992:Terminology and equivalence
551:By mechanism of combination
322:Proportional representation
6188:
5673:Real business-cycle theory
4867:Condorcet winner criterion
4558:First-past-the-post voting
4341:Cambridge University Press
2523:interpersonally-comparable
2020:first-preference plurality
749:Multiple districts paradox
480:Fractional approval voting
468:Interactive representation
29:
6113:
5022:
5014:Voting systems by country
4917:Mutual majority criterion
4872:Condorcet loser criterion
4818:Vote linkage mixed system
4730:Largest remainders method
4457:
4325:–88. Reprinted in (1986)
4110:Quesada, Antonio (2002).
3689:axioms of rational choice
2713:) social orderings makes
2696:ordinal utility functions
2356:"Social welfare function"
1914:). They are also used by
696:Paradoxes and pathologies
545:Mixed-member proportional
540:Mixed-member majoritarian
535:By results of combination
426:Approval-based committees
4907:Majority loser criterion
4793:Additional member system
4751:Hagenbach-Bischoff quota
4670:Single transferable vote
4595:Positional voting system
4531:Minimax Condorcet method
4489:Combined approval voting
4007:Distribution (economics)
3883:Nash bargaining solution
3504:reordering or relabeling
2490:social welfare function,
2449:may contain suggestions.
2434:may need to be rewritten
1081:JEL classification codes
875:Condorcet's jury theorem
676:Double simultaneous vote
651:Rural–urban proportional
646:Dual-member proportional
608:
597:
564:Parallel (superposition)
456:Fractional social choice
443:Expanding approvals rule
272:
257:
242:
173:
162:
138:
5313:Industrial organization
5136:Computational economics
4932:Resolvability criterion
4922:Participation criterion
4897:Later-no-harm criterion
4713:Highest averages method
4163:, 1951, 2nd ed., 1963,
4087:Public Sector Economics
3907:{\displaystyle \eta =1}
3874:{\displaystyle \eta =0}
3678:
3461:Suppose we are given a
1873:social welfare function
1267:Industrial organization
1124:Computational economics
802:Tyranny of the majority
579:Fusion (majority bonus)
396:Quota-remainder methods
18:Social ranking function
6172:Mathematical economics
5518:Modern monetary theory
5183:Experimental economics
5153:Pluralism in economics
5126:Mathematical economics
4973:First-preference votes
4912:Monotonicity criterion
4882:Independence of clones
4585:Simple majoritarianism
4227:Pattanaik, Prasanta K.
4200:On Economic Inequality
3975:
3958:Pigou–Dalton principle
3941:
3908:
3875:
3842:
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3718:
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3439:
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3246:
3226:
3191:
3105:
3021:
2993:
2940:
2920:
2900:
2879:is social welfare and
2873:
2850:
2835:
2782:or per capita income.
1119:Experimental economics
936:Mathematics portal
842:Majority impossibility
831:Impossibility theorems
627:Negative vote transfer
448:Method of equal shares
69:
4877:Consistency criterion
4798:Alternative vote plus
4563:Instant-runoff voting
4133:Herve Moulin (2004).
3976:
3974:{\displaystyle \eta }
3942:
3909:
3876:
3843:
3808:
3719:
3663:
3618:
3468:on utility profiles.
3440:
3344:
3247:
3227:
3225:{\displaystyle (1-G)}
3192:
3106:
3022:
2973:
2941:
2921:
2901:
2899:{\displaystyle Y_{i}}
2874:
2851:
2815:
1949:) functions use only
739:Best-is-worst paradox
728:Pathological response
463:Direct representation
116:Single-winner methods
68:
6167:Social choice theory
5392:Social choice theory
5148:Behavioral economics
5131:Complexity economics
4947:Seats-to-votes ratio
4718:Webster/Sainte-Laguë
4194:James E. Foster and
4042:Social choice theory
3965:
3925:
3892:
3859:
3823:
3761:
3717:{\displaystyle w(u)}
3699:
3574:
3521:: for every profile
3367:
3271:
3236:
3204:
3135:
3120:uncertainty aversion
3041:
2954:
2930:
2910:
2883:
2863:
2806:
2624:possibility function
2539:, often treated the
2517:Bergson argued that
2488:introduced the term
2341:improve this article
2032:abuse of terminology
1912:income distributions
1869:social choice theory
1346:Social choice theory
923:Economics portal
870:Median voter theorem
89:Comparative politics
5476:American (National)
5176:Economic statistics
4927:Plurality criterion
4526:Kemeny–Young method
4321:, N.S., 44(173), p
4263:Also available as:
4027:Justice (economics)
3992:Aggregation problem
3753:isoelastic function
3463:preference relation
2484:In a 1938 article,
2054:
1813:Business portal
1134:Operations research
1114:National accounting
911:Politics portal
622:Vote linkage system
593:Seat linkage system
180:Ranked-choice (RCV)
4968:Election threshold
4902:Majority criterion
4578:Supplementary vote
4265:a journal article.
4239:Blume, Lawrence E.
4235:Durlauf, Steven N.
4116:Economics Bulletin
3971:
3955:If we require the
3937:
3904:
3871:
3838:
3803:
3714:
3679:Harsanyi's theorem
3658:
3491:Pareto improvement
3435:
3339:
3242:
3222:
3187:
3101:
3017:
2936:
2916:
2896:
2869:
2846:
2570:Pareto improvement
2285:You can assist by
2053:
1144:Industrial complex
1139:Middle income trap
807:Discursive dilemma
766:Lesser evil voting
641:Supermixed systems
344:Largest remainders
202:Round-robin voting
70:
6162:Welfare economics
6149:
6148:
5680:New institutional
5039:
5038:
4937:Reversal symmetry
4846:Cumulative voting
4828:Semi-proportional
4803:Mixed single vote
4769:
4768:
4645:Mixed single vote
4553:Exhaustive ballot
4516:Copeland's method
4511:Condorcet methods
4451:Electoral systems
4299:Paul A. Samuelson
4282:, 1935, 2nd ed..
4274:Jan de Van Graaff
4096:978-0-230-52223-7
4047:Welfare economics
4022:Gorman polar form
4017:Extended sympathy
3801:
3411:
3315:
3245:{\displaystyle G}
3170:
3015:
2971:
2939:{\displaystyle n}
2919:{\displaystyle i}
2872:{\displaystyle W}
2756:Pareto efficiency
2730:rational behavior
2684:
2683:
2565:Pareto efficiency
2519:welfare economics
2482:
2481:
2474:
2464:
2463:
2438:quality standards
2417:
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2152:
2151:
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2105:
1865:welfare economics
1861:
1860:
970:
969:
857:Gibbard's theorem
797:Dominance paradox
734:Perverse response
438:Phragmen's method
304:Majority judgment
232:Positional voting
190:Condorcet methods
58:electoral systems
32:electoral systems
16:(Redirected from
6179:
5353:Natural resource
5188:Economic history
5114:Mechanism design
5066:
5059:
5052:
5043:
4978:Liquid democracy
4630:
4610:Two-round system
4521:Dodgson's method
4444:
4437:
4430:
4421:
4358:Economic Journal
4293:Economic Journal
4256:
4214:John C. Harsanyi
4161:Kenneth J. Arrow
4149:
4148:
4130:
4124:
4123:
4107:
4101:
4100:
4082:
4076:
4063:
4012:Economic welfare
3980:
3978:
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3693:utilitarian rule
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3118:extreme form of
3110:
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2870:
2855:
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2852:
2847:
2845:
2844:
2834:
2829:
2776:cardinal utility
2766:Cardinal welfare
2760:utilitarian rule
2644:
2620:welfare function
2526:cardinal utility
2477:
2470:
2459:
2456:
2450:
2427:
2419:
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2196:
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2114:
2055:
1853:
1846:
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1825:Money portal
1823:
1822:
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1811:
1810:
1307:Natural resource
1099:Economic systems
995:
972:
962:
955:
948:
934:
933:
921:
920:
909:
908:
864:Positive results
759:Strategic voting
656:Majority jackpot
613:
602:
473:Liquid democracy
349:National remnant
339:Highest averages
276:
261:
246:
178:
169:Alternative vote
167:
151:Partisan primary
143:
84:Mechanism design
37:
21:
6187:
6186:
6182:
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6180:
6178:
6177:
6176:
6152:
6151:
6150:
6145:
6142:Business portal
6109:
6108:
6107:
6067:
5831:von Böhm-Bawerk
5719:
5718:
5709:
5481:Ancient thought
5459:
5458:
5452:
5443:
5442:
5441:
5192:
5157:
5109:Contract theory
5094:Decision theory
5075:
5070:
5040:
5035:
5018:
4997:
4951:
4942:Smith criterion
4855:
4822:
4783:Parallel voting
4765:
4761:Imperiali quota
4734:
4701:
4619:
4573:Contingent vote
4536:Nanson's method
4494:Unified primary
4484:Approval voting
4470:
4453:
4448:
4399:Kotaro Suzumura
4354:Sen, Amartya K.
4295:, 43(4), 635–41
4253:
4225:
4157:
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4109:
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4104:
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4079:
4064:
4060:
4056:
4051:
4032:Liberal paradox
3987:
3963:
3962:
3923:
3922:
3921:The limit when
3890:
3889:
3857:
3856:
3821:
3820:
3819:The limit when
3790:
3767:
3766:
3759:
3758:
3734:
3732:Non-utilitarian
3697:
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2780:life expectancy
2768:
2653:consumer theory
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2256:
2245:
2239:
2236:
2228:help improve it
2225:
2216:
2212:
2175:
2171:
2164:
2162:Ordinal welfare
2048:between the two
2040:
1994:
1927:consumer choice
1875:—also called a
1857:
1819:
1817:
1805:
1798:
1797:
1768:
1758:
1757:
1756:
1755:
1519:von Böhm-Bawerk
1407:
1396:
1395:
1157:
1149:
1148:
1104:Economic growth
1094:
1086:
1085:
1027:
1025:classifications
966:
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927:
915:
903:
895:
894:
861:
837:Arrow's theorem
827:
817:
816:
785:
755:
744:No-show paradox
725:
711:Cloning paradox
701:Spoiler effects
698:
688:
687:
662:
549:
532:
522:
521:
494:
485:Maximal lottery
452:
433:Thiele's method
422:
392:
324:
314:
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299:Approval voting
287:Cardinal voting
283:
228:
222:Maximal lottery
186:
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35:
28:
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22:
15:
12:
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5:
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5545:Disequilibrium
5542:
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5505:
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5495:
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5358:Organizational
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5310:
5305:
5300:
5295:
5290:
5285:
5280:
5275:
5270:
5265:
5260:
5255:
5250:
5245:
5240:
5235:
5230:
5225:
5220:
5215:
5210:
5204:
5203:
5202:
5200:
5194:
5193:
5191:
5190:
5185:
5180:
5179:
5178:
5167:
5165:
5159:
5158:
5156:
5155:
5150:
5145:
5144:
5143:
5133:
5128:
5123:
5121:Macroeconomics
5118:
5117:
5116:
5111:
5106:
5101:
5096:
5089:Microeconomics
5085:
5083:
5077:
5076:
5071:
5069:
5068:
5061:
5054:
5046:
5037:
5036:
5023:
5020:
5019:
5017:
5016:
5011:
5005:
5003:
4999:
4998:
4996:
4995:
4990:
4985:
4980:
4975:
4970:
4965:
4959:
4957:
4953:
4952:
4950:
4949:
4944:
4939:
4934:
4929:
4924:
4919:
4914:
4909:
4904:
4899:
4894:
4889:
4884:
4879:
4874:
4869:
4863:
4861:
4857:
4856:
4854:
4853:
4848:
4843:
4841:Limited voting
4838:
4832:
4830:
4824:
4823:
4821:
4820:
4815:
4810:
4805:
4800:
4795:
4790:
4785:
4779:
4777:
4771:
4770:
4767:
4766:
4764:
4763:
4758:
4753:
4748:
4742:
4740:
4736:
4735:
4733:
4732:
4727:
4726:
4725:
4720:
4709:
4707:
4703:
4702:
4700:
4699:
4694:
4689:
4688:
4687:
4682:
4677:
4667:
4662:
4657:
4652:
4647:
4642:
4636:
4634:
4627:
4621:
4620:
4618:
4617:
4612:
4607:
4602:
4597:
4592:
4587:
4582:
4581:
4580:
4575:
4570:
4568:Coombs' method
4560:
4555:
4550:
4549:
4548:
4546:Schulze method
4543:
4538:
4533:
4528:
4523:
4518:
4508:
4506:Bucklin voting
4503:
4498:
4497:
4496:
4491:
4480:
4478:
4472:
4471:
4458:
4455:
4454:
4449:
4447:
4446:
4439:
4432:
4424:
4418:
4417:
4416:, v. 4, 418–20
4410:
4396:
4384:_____ (1982).
4382:
4367:_____, 1970 ,
4365:
4351:
4333:
4315:
4296:
4289:
4280:Lionel Robbins
4277:
4270:
4269:
4268:
4267:
4258:
4257:
4251:
4223:
4222:, v. 2, 955–58
4211:
4192:
4186:
4176:
4156:
4153:
4151:
4150:
4143:
4125:
4102:
4095:
4077:
4066:Amartya K. Sen
4057:
4055:
4052:
4050:
4049:
4044:
4039:
4034:
4029:
4024:
4019:
4014:
4009:
4004:
3999:
3994:
3988:
3986:
3983:
3970:
3953:
3952:
3936:
3933:
3930:
3919:
3903:
3900:
3897:
3886:
3870:
3867:
3864:
3853:
3837:
3834:
3831:
3828:
3799:
3796:
3793:
3788:
3785:
3780:
3777:
3774:
3770:
3733:
3730:
3713:
3710:
3707:
3704:
3680:
3677:
3669:
3668:
3657:
3652:
3648:
3644:
3641:
3636:
3631:
3628:
3625:
3621:
3617:
3614:
3609:
3605:
3601:
3598:
3595:
3590:
3586:
3582:
3579:
3458:
3455:
3446:
3445:
3430:
3426:
3422:
3417:
3410:
3407:
3402:
3396:
3393:
3390:
3387:
3384:
3381:
3378:
3373:
3350:
3349:
3334:
3330:
3326:
3321:
3314:
3311:
3306:
3300:
3297:
3294:
3291:
3288:
3285:
3282:
3277:
3241:
3221:
3218:
3215:
3212:
3209:
3198:
3197:
3186:
3183:
3180:
3177:
3174:
3169:
3166:
3161:
3155:
3152:
3149:
3146:
3141:
3112:
3111:
3100:
3095:
3091:
3087:
3084:
3081:
3076:
3072:
3068:
3063:
3059:
3055:
3052:
3049:
3046:
3028:
3027:
3014:
3011:
3006:
3001:
2997:
2991:
2986:
2983:
2980:
2976:
2970:
2967:
2962:
2959:
2935:
2915:
2893:
2889:
2868:
2857:
2856:
2843:
2839:
2833:
2828:
2825:
2822:
2818:
2814:
2811:
2767:
2764:
2703:Lionel Robbins
2682:
2681:
2680:
2679:
2676:
2673:
2667:
2651:. Relative to
2613:
2612:
2609:
2578:Paul Samuelson
2533:utilitarianism
2515:
2514:
2511:
2508:
2494:differentiable
2480:
2479:
2462:
2461:
2431:
2429:
2422:
2415:
2414:
2329:
2327:
2320:
2313:
2312:
2274:
2272:
2265:
2258:
2257:
2219:
2217:
2210:
2205:
2179:
2178:
2176:
2169:
2163:
2160:
2150:
2149:
2146:
2142:
2141:
2136:
2132:
2131:
2126:
2122:
2121:
2118:
2104:
2103:
2100:
2097:
2093:
2092:
2087:
2082:
2078:
2077:
2072:
2069:
2065:
2064:
2061:
2058:
2044:instant-runoff
2039:
2036:
2024:
2023:
2012:
2005:
1993:
1990:
1975:
1974:
1954:
1859:
1858:
1856:
1855:
1848:
1841:
1833:
1830:
1829:
1828:
1827:
1815:
1800:
1799:
1796:
1795:
1790:
1780:
1775:
1769:
1764:
1763:
1760:
1759:
1754:
1753:
1746:
1741:
1736:
1731:
1726:
1721:
1716:
1711:
1706:
1701:
1696:
1691:
1686:
1681:
1676:
1671:
1666:
1661:
1656:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1581:
1576:
1571:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1410:
1409:
1408:
1402:
1401:
1398:
1397:
1394:
1393:
1388:
1383:
1378:
1373:
1368:
1363:
1358:
1353:
1348:
1339:
1334:
1329:
1324:
1319:
1314:
1312:Organizational
1309:
1304:
1299:
1294:
1289:
1284:
1279:
1274:
1269:
1264:
1259:
1254:
1249:
1244:
1239:
1234:
1229:
1224:
1219:
1214:
1209:
1204:
1199:
1194:
1189:
1184:
1179:
1174:
1169:
1164:
1158:
1156:By application
1155:
1154:
1151:
1150:
1147:
1146:
1141:
1136:
1131:
1126:
1121:
1116:
1111:
1106:
1101:
1095:
1092:
1091:
1088:
1087:
1084:
1083:
1078:
1073:
1068:
1063:
1058:
1049:
1044:
1039:
1034:
1028:
1022:
1021:
1018:
1017:
1016:
1015:
1010:
1005:
997:
996:
988:
987:
981:
980:
968:
967:
965:
964:
957:
950:
942:
939:
938:
926:
925:
913:
900:
897:
896:
893:
892:
887:
882:
877:
872:
860:
859:
854:
849:
844:
839:
828:
823:
822:
819:
818:
815:
814:
809:
804:
799:
784:
783:
781:Turkey-raising
778:
773:
768:
754:
753:
752:
751:
741:
736:
724:
723:
721:Center squeeze
718:
713:
708:
706:Spoiler effect
699:
694:
693:
690:
689:
686:
685:
680:
679:
678:
665:By ballot type
661:
660:
659:
658:
653:
648:
638:
637:
636:
635:
634:
629:
619:
618:
617:
606:
583:
582:
581:
576:
571:
566:
548:
547:
542:
533:
528:
527:
524:
523:
520:
519:
517:Limited voting
514:
513:
512:
493:
492:
487:
482:
477:
476:
475:
470:
451:
450:
445:
440:
435:
421:
420:
415:
410:
405:
391:
390:
389:
388:
386:Localized list
383:
378:
373:
368:
358:
357:
356:
354:Biproportional
351:
346:
341:
325:
320:
319:
316:
315:
312:
311:
306:
301:
296:
282:
281:
266:
251:
227:
226:
225:
224:
219:
214:
209:
199:
185:
184:
183:
182:
171:
158:Instant-runoff
155:
154:
153:
145:Jungle primary
132:
121:Single vote -
119:
114:
113:
110:
109:
107:
106:
96:
91:
86:
81:
75:
72:
71:
61:
60:
50:
49:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6184:
6173:
6170:
6168:
6165:
6163:
6160:
6159:
6157:
6143:
6140:
6138:
6135:
6133:
6130:
6128:
6125:
6123:
6120:
6118:
6115:
6112:
6104:
6101:
6098:
6094:
6091:
6089:
6086:
6084:
6081:
6080:
6076:
6074:
6070:
6064:
6063:
6059:
6057:
6054:
6052:
6049:
6047:
6044:
6042:
6039:
6037:
6034:
6032:
6029:
6027:
6024:
6022:
6019:
6017:
6014:
6012:
6009:
6007:
6004:
6002:
5999:
5997:
5994:
5992:
5989:
5987:
5984:
5982:
5979:
5977:
5974:
5972:
5969:
5967:
5964:
5962:
5959:
5957:
5954:
5952:
5949:
5947:
5944:
5942:
5939:
5937:
5934:
5932:
5929:
5927:
5924:
5922:
5919:
5917:
5914:
5912:
5909:
5907:
5904:
5902:
5899:
5897:
5894:
5892:
5889:
5887:
5884:
5882:
5879:
5877:
5874:
5872:
5869:
5867:
5864:
5862:
5859:
5857:
5854:
5852:
5849:
5847:
5844:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5822:
5819:
5817:
5814:
5812:
5809:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5789:
5787:
5784:
5782:
5779:
5777:
5774:
5772:
5769:
5767:
5764:
5762:
5759:
5757:
5754:
5752:
5749:
5747:
5744:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5726:de Mandeville
5724:
5723:
5721:
5717:
5712:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5681:
5678:
5674:
5671:
5670:
5669:
5668:New classical
5666:
5662:
5659:
5658:
5657:
5654:
5652:
5649:
5647:
5644:
5640:
5637:
5636:
5635:
5632:
5630:
5627:
5625:
5624:Malthusianism
5622:
5616:
5613:
5612:
5611:
5608:
5606:
5603:
5600:
5596:
5593:
5592:
5591:
5588:
5586:
5585:Institutional
5583:
5581:
5578:
5576:
5573:
5571:
5568:
5566:
5563:
5561:
5558:
5556:
5553:
5551:
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5531:
5528:
5526:
5523:
5519:
5516:
5515:
5514:
5511:
5509:
5506:
5504:
5501:
5499:
5496:
5492:
5489:
5488:
5487:
5484:
5482:
5479:
5477:
5474:
5472:
5469:
5467:
5464:
5463:
5461:
5456:
5451:
5446:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5393:
5389:
5388:Public choice
5386:
5384:
5381:
5379:
5376:
5374:
5371:
5369:
5366:
5364:
5363:Participation
5361:
5359:
5356:
5354:
5351:
5349:
5346:
5344:
5341:
5339:
5336:
5334:
5331:
5329:
5326:
5324:
5323:Institutional
5321:
5319:
5316:
5314:
5311:
5309:
5306:
5304:
5301:
5299:
5296:
5294:
5291:
5289:
5286:
5284:
5281:
5279:
5276:
5274:
5273:Expeditionary
5271:
5269:
5266:
5264:
5263:Environmental
5261:
5259:
5256:
5254:
5251:
5249:
5246:
5244:
5241:
5239:
5236:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5209:
5206:
5205:
5201:
5199:
5195:
5189:
5186:
5184:
5181:
5177:
5174:
5173:
5172:
5169:
5168:
5166:
5164:
5160:
5154:
5151:
5149:
5146:
5142:
5139:
5138:
5137:
5134:
5132:
5129:
5127:
5124:
5122:
5119:
5115:
5112:
5110:
5107:
5105:
5102:
5100:
5097:
5095:
5092:
5091:
5090:
5087:
5086:
5084:
5082:
5078:
5074:
5067:
5062:
5060:
5055:
5053:
5048:
5047:
5044:
5034:
5033:
5028:
5027:
5021:
5015:
5012:
5010:
5007:
5006:
5004:
5000:
4994:
4991:
4989:
4986:
4984:
4981:
4979:
4976:
4974:
4971:
4969:
4966:
4964:
4961:
4960:
4958:
4954:
4948:
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4923:
4920:
4918:
4915:
4913:
4910:
4908:
4905:
4903:
4900:
4898:
4895:
4893:
4890:
4888:
4885:
4883:
4880:
4878:
4875:
4873:
4870:
4868:
4865:
4864:
4862:
4858:
4852:
4849:
4847:
4844:
4842:
4839:
4837:
4834:
4833:
4831:
4829:
4825:
4819:
4816:
4814:
4811:
4809:
4806:
4804:
4801:
4799:
4796:
4794:
4791:
4789:
4786:
4784:
4781:
4780:
4778:
4776:
4772:
4762:
4759:
4757:
4754:
4752:
4749:
4747:
4744:
4743:
4741:
4737:
4731:
4728:
4724:
4721:
4719:
4716:
4715:
4714:
4711:
4710:
4708:
4704:
4698:
4695:
4693:
4690:
4686:
4683:
4681:
4678:
4676:
4673:
4672:
4671:
4668:
4666:
4663:
4661:
4658:
4656:
4653:
4651:
4648:
4646:
4643:
4641:
4638:
4637:
4635:
4631:
4628:
4626:
4622:
4616:
4613:
4611:
4608:
4606:
4603:
4601:
4598:
4596:
4593:
4591:
4588:
4586:
4583:
4579:
4576:
4574:
4571:
4569:
4566:
4565:
4564:
4561:
4559:
4556:
4554:
4551:
4547:
4544:
4542:
4539:
4537:
4534:
4532:
4529:
4527:
4524:
4522:
4519:
4517:
4514:
4513:
4512:
4509:
4507:
4504:
4502:
4499:
4495:
4492:
4490:
4487:
4486:
4485:
4482:
4481:
4479:
4477:
4476:Single-winner
4473:
4469:
4467:
4463:
4456:
4452:
4445:
4440:
4438:
4433:
4431:
4426:
4425:
4422:
4415:
4411:
4408:
4405:, 47(186), p
4404:
4400:
4397:
4395:
4391:
4388:, MIT Press.
4387:
4383:
4381:
4380:0-444-85127-5
4377:
4373:
4372:(description)
4370:
4366:
4363:
4359:
4355:
4352:
4350:
4347:, pp. 3
4346:
4342:
4338:
4334:
4332:
4328:
4324:
4320:
4316:
4314:
4313:0-674-31301-1
4310:
4306:
4305:
4300:
4297:
4294:
4290:
4287:
4286:
4281:
4278:
4275:
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4260:
4259:
4254:
4252:9780333786765
4248:
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4212:
4209:
4208:0-19-828193-5
4205:
4201:
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4190:
4187:
4184:
4180:
4179:Abram Bergson
4177:
4175:
4174:0-300-01364-7
4171:
4168:
4167:
4162:
4159:
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4146:
4144:9780262134231
4140:
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4018:
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4008:
4005:
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4000:
3998:
3995:
3993:
3990:
3989:
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3328:
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3181:
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3131:
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3129:
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2999:
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2800:
2798:
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2783:
2781:
2777:
2773:
2765:
2763:
2761:
2757:
2753:
2749:
2745:
2741:
2740:John Harsanyi
2737:
2735:
2731:
2727:
2724:
2720:
2716:
2712:
2708:
2704:
2699:
2697:
2692:
2688:
2687:Kenneth Arrow
2677:
2674:
2672:
2668:
2666:
2661:
2660:
2658:
2654:
2650:
2646:
2645:
2642:
2639:
2634:
2629:
2625:
2621:
2616:
2610:
2607:
2606:
2605:
2603:
2599:
2594:
2591:
2587:
2583:
2579:
2575:
2574:substantively
2571:
2567:
2566:
2560:
2558:
2554:
2553:unfalsifiable
2550:
2546:
2542:
2538:
2534:
2529:
2527:
2524:
2520:
2512:
2509:
2506:
2505:
2504:
2501:
2499:
2495:
2491:
2487:
2486:Abram Bergson
2476:
2473:
2458:
2448:
2444:
2439:
2435:
2432:This section
2430:
2426:
2421:
2420:
2411:
2408:
2400:
2389:
2386:
2382:
2379:
2375:
2372:
2368:
2365:
2361:
2358: –
2357:
2353:
2352:Find sources:
2346:
2342:
2336:
2335:
2330:This section
2328:
2324:
2319:
2318:
2309:
2306:
2298:
2288:
2282:
2280:
2275:This section
2273:
2264:
2263:
2254:
2251:
2243:
2233:
2229:
2223:
2220:This section
2218:
2209:
2208:
2203:
2201:
2194:
2193:
2188:
2187:
2182:
2177:
2168:
2167:
2161:
2159:
2157:
2147:
2144:
2143:
2140:
2137:
2134:
2133:
2130:
2127:
2124:
2123:
2119:
2116:
2115:
2112:
2109:
2101:
2098:
2095:
2094:
2091:
2088:
2086:
2083:
2080:
2079:
2076:
2073:
2070:
2067:
2066:
2062:
2059:
2057:
2056:
2051:
2049:
2045:
2037:
2035:
2033:
2028:
2021:
2017:
2013:
2010:
2006:
2003:
1999:
1998:
1997:
1991:
1989:
1987:
1983:
1979:
1972:
1968:
1964:
1960:
1959:
1955:
1952:
1948:
1947:ranked voting
1944:
1943:
1939:
1938:
1937:
1934:
1932:
1928:
1923:
1921:
1917:
1913:
1908:
1903:
1900:
1896:
1893:
1889:
1885:
1881:
1878:
1874:
1870:
1866:
1854:
1849:
1847:
1842:
1840:
1835:
1834:
1832:
1831:
1826:
1816:
1814:
1809:
1804:
1803:
1802:
1801:
1794:
1791:
1788:
1784:
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1779:
1776:
1774:
1771:
1770:
1767:
1762:
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1752:
1751:
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1730:
1727:
1725:
1722:
1720:
1717:
1715:
1712:
1710:
1707:
1705:
1702:
1700:
1697:
1695:
1692:
1690:
1687:
1685:
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1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
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1647:
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1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1590:
1587:
1585:
1582:
1580:
1577:
1575:
1572:
1570:
1567:
1565:
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1435:
1432:
1430:
1427:
1425:
1422:
1420:
1417:
1415:
1414:de Mandeville
1412:
1411:
1406:
1400:
1399:
1392:
1389:
1387:
1384:
1382:
1379:
1377:
1374:
1372:
1369:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1343:
1342:Public choice
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1323:
1320:
1318:
1317:Participation
1315:
1313:
1310:
1308:
1305:
1303:
1300:
1298:
1295:
1293:
1290:
1288:
1285:
1283:
1280:
1278:
1277:Institutional
1275:
1273:
1270:
1268:
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1227:Expeditionary
1225:
1223:
1220:
1218:
1217:Environmental
1215:
1213:
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1183:
1180:
1178:
1175:
1173:
1170:
1168:
1165:
1163:
1160:
1159:
1153:
1152:
1145:
1142:
1140:
1137:
1135:
1132:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1097:
1096:
1090:
1089:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1053:
1050:
1048:
1047:International
1045:
1043:
1040:
1038:
1035:
1033:
1030:
1029:
1026:
1023:Branches and
1020:
1019:
1014:
1011:
1009:
1006:
1004:
1001:
1000:
999:
998:
994:
990:
989:
986:
982:
978:
974:
973:
963:
958:
956:
951:
949:
944:
943:
941:
940:
937:
932:
924:
919:
914:
912:
907:
902:
901:
899:
898:
891:
888:
886:
883:
881:
880:May's theorem
878:
876:
873:
871:
868:
867:
866:
865:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
834:
833:
832:
826:
821:
820:
813:
810:
808:
805:
803:
800:
798:
795:
794:
793:
792:
791:
790:majority rule
788:Paradoxes of
782:
779:
777:
774:
772:
769:
767:
764:
763:
762:
761:
760:
750:
747:
746:
745:
742:
740:
737:
735:
732:
731:
730:
729:
722:
719:
717:
714:
712:
709:
707:
704:
703:
702:
697:
692:
691:
684:
681:
677:
674:
673:
672:
669:
668:
667:
666:
657:
654:
652:
649:
647:
644:
643:
642:
639:
633:
630:
628:
625:
624:
623:
620:
616:
611:
607:
605:
600:
596:
595:
594:
591:
590:
589:
588:
584:
580:
577:
575:
572:
570:
567:
565:
562:
561:
560:
559:
554:
553:
552:
546:
543:
541:
538:
537:
536:
531:
530:Mixed systems
526:
525:
518:
515:
511:
508:
507:
506:
503:
502:
501:
500:
499:
491:
490:Random ballot
488:
486:
483:
481:
478:
474:
471:
469:
466:
465:
464:
461:
460:
459:
458:
457:
449:
446:
444:
441:
439:
436:
434:
431:
430:
429:
428:
427:
419:
416:
414:
411:
409:
406:
404:
401:
400:
399:
398:
397:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
363:
362:
359:
355:
352:
350:
347:
345:
342:
340:
337:
336:
335:
334:Apportionment
332:
331:
330:
329:
323:
318:
317:
310:
307:
305:
302:
300:
297:
295:
292:
291:
290:
289:
288:
279:
275:
270:
269:Antiplurality
267:
264:
260:
255:
252:
249:
245:
240:
237:
236:
235:
234:
233:
223:
220:
218:
215:
213:
210:
208:
205:
204:
203:
200:
198:
197:Condorcet-IRV
195:
194:
193:
192:
191:
181:
176:
172:
170:
165:
161:
160:
159:
156:
152:
149:
148:
146:
141:
136:
133:
131:
128:
127:
126:
124:
117:
112:
111:
104:
100:
97:
95:
92:
90:
87:
85:
82:
80:
79:Social choice
77:
76:
74:
73:
67:
63:
62:
59:
55:
54:Social choice
51:
47:
43:
39:
38:
33:
19:
6137:Publications
6093:Publications
6060:
5656:Neoclassical
5646:Mercantilism
5555:Evolutionary
5417:Sociological
5390: /
5288:Geographical
5268:Evolutionary
5243:Digitization
5208:Agricultural
5171:Econometrics
5099:Price theory
5030:
5024:
4640:Mixed-member
4625:Proportional
4600:Score voting
4541:Ranked pairs
4460:Part of the
4459:
4413:
4402:
4385:
4368:
4357:
4344:
4336:
4326:
4318:
4302:
4292:
4283:
4242:
4231:(definition)
4230:
4217:
4199:
4182:
4164:
4134:
4128:
4119:
4115:
4105:
4086:
4080:
4074:Description.
4069:
4061:
3956:
3954:
3948:
3849:
3814:
3757:
3751:must be the
3748:
3746:
3741:
3739:
3735:
3682:
3672:
3670:
3564:
3562:
3558:separability
3557:
3553:
3548:
3544:
3541:
3539:
3530:
3526:
3522:
3518:
3516:
3511:
3507:
3498:
3495:
3486:
3482:Monotonicity
3481:
3478:
3469:
3465:
3460:
3449:
3447:
3353:
3351:
3199:
3124:
3116:
3113:
3029:
2858:
2790:
2787:
2784:
2771:
2769:
2738:
2725:
2707:behaviorists
2700:
2685:
2670:
2664:
2656:
2637:
2632:
2623:
2619:
2617:
2614:
2601:
2595:
2589:
2585:
2581:
2573:
2569:
2563:
2561:
2544:
2530:
2522:
2516:
2502:
2489:
2483:
2468:
2452:
2443:You can help
2433:
2403:
2394:
2384:
2377:
2370:
2363:
2351:
2339:Please help
2334:verification
2331:
2301:
2292:
2279:copy editing
2277:may require
2276:
2246:
2237:
2221:
2197:
2190:
2184:
2183:Please help
2180:
2153:
2138:
2128:
2110:
2107:
2089:
2084:
2074:
2042:Consider an
2041:
2029:
2025:
2015:
2008:
2001:
1995:
1976:
1970:
1963:rated voting
1957:
1953:information.
1941:
1935:
1930:
1924:
1904:
1894:
1891:
1887:
1883:
1879:
1876:
1872:
1862:
1783:Publications
1748:
1371:Sociological
1344: /
1242:Geographical
1222:Evolutionary
1197:Digitization
1162:Agricultural
1066:Mathematical
1037:Econometrics
863:
862:
829:
787:
786:
771:Exaggeration
757:
756:
727:
726:
700:
664:
663:
632:Mixed ballot
587:Compensatory
585:
558:compensatory
555:
550:
534:
496:
495:
454:
453:
424:
423:
394:
393:
381:List-free PR
326:
294:Score voting
285:
284:
230:
229:
217:Ranked pairs
188:
187:
120:
5931:von Neumann
5700:Supply-side
5685:Physiocracy
5629:Marginalism
5318:Information
5258:Engineering
5238:Development
5233:Demographic
5104:Game theory
5081:Theoretical
4983:Spoilt vote
4746:Droop quota
4685:Schulze STV
4660:Rural–urban
4605:STAR voting
4501:Borda count
4390:Description
4360:, 73(292),
4196:Amartya Sen
3916:utilitarian
3914:we get the
3881:we get the
3685:Dutch Books
3535:closed sets
3474:total order
3262:Theil index
3126:Amartya Sen
2793:utilitarian
2748:uncertainty
2596:Samuelson (
2557:behaviorism
1986:second-best
1619:von Neumann
1272:Information
1212:Engineering
1192:Development
1187:Demographic
1129:Game theory
1071:Methodology
671:Single vote
574:Conditional
569:Coexistence
418:Quota Borda
408:Schulze STV
366:Closed list
309:STAR voting
254:Borda count
6156:Categories
6088:Economists
5961:Schumacher
5866:Schumpeter
5836:von Wieser
5756:von ThĂĽnen
5716:Economists
5615:Circuitism
5580:Humanistic
5575:Historical
5550:Ecological
5540:Democratic
5513:Chartalism
5503:Behavioral
5466:Mainstream
5427:Statistics
5422:Solidarity
5343:Managerial
5308:Humanistic
5303:Historical
5248:Ecological
5213:Behavioral
5002:Comparison
4756:Hare quota
4706:Allocation
4692:Spare vote
4680:Hare-Clark
4650:Party-list
4155:References
4122:(16): 1–7.
3519:Continuity
3472:is a weak
3254:Gini index
3032:John Rawls
2797:Benthamite
2705:and other
2657:individual
2455:March 2024
2397:March 2024
2367:newspapers
2295:March 2024
2287:editing it
2240:March 2024
2186:improve it
2117:Runner-up
2090:Eliminated
1931:individual
1916:democratic
1907:economists
1778:Economists
1649:Schumacher
1554:Schumpeter
1524:von Wieser
1444:von ThĂĽnen
1405:economists
1381:Statistics
1376:Solidarity
1297:Managerial
1262:Humanistic
1257:Historical
1202:Ecological
1167:Behavioral
1061:Mainstream
776:Truncation
505:Cumulative
328:Party-list
103:By country
94:Comparison
6006:Greenspan
5971:Samuelson
5951:Galbraith
5921:Tinbergen
5861:von Mises
5856:Heckscher
5816:Edgeworth
5695:Stockholm
5690:Socialist
5590:Keynesian
5570:Happiness
5530:Classical
5491:Mutualism
5486:Anarchist
5471:Heterodox
5368:Personnel
5328:Knowledge
5293:Happiness
5283:Financial
5253:Education
5228:Democracy
5163:Empirical
5073:Economics
4993:Unseating
4988:Sortition
4590:Plurality
4466:Economics
4403:Economica
4319:Economica
4068:, 1970 ,
3969:η
3951:ordering.
3935:∞
3932:→
3929:η
3896:η
3863:η
3852:ordering.
3836:∞
3833:−
3830:→
3827:η
3798:η
3795:−
3784:−
3779:η
3776:−
3620:∑
3597:…
3421:−
3409:¯
3392:−
3325:−
3313:¯
3296:−
3214:−
3179:−
3168:¯
3083:⋯
3013:¯
2975:∑
2817:∑
2752:coherence
2732:, called
2691:1963 book
2628:arguments
2582:necessary
2498:resources
2447:talk page
2192:talk page
2014:A social
2007:A social
2000:A social
1920:elections
1694:Greenspan
1659:Samuelson
1639:Galbraith
1609:Tinbergen
1549:von Mises
1544:Heckscher
1504:Edgeworth
1322:Personnel
1282:Knowledge
1247:Happiness
1237:Financial
1207:Education
1182:Democracy
1076:Political
1042:Heterodox
985:Economics
683:Dual-vote
376:Panachage
371:Open list
361:List type
239:Plurality
135:Two-round
123:plurality
46:Economics
6117:Category
6097:journals
6083:Glossary
6036:Stiglitz
6001:Rothbard
5981:Buchanan
5966:Friedman
5956:Koopmans
5946:Leontief
5926:Robinson
5811:Marshall
5661:Lausanne
5565:Georgism
5560:Feminist
5508:Buddhist
5498:Austrian
5397:Regional
5373:Planning
5348:Monetary
5278:Feminist
5223:Cultural
5218:Business
4860:Criteria
4813:Scorporo
4462:politics
4288:, ch. VI
4241:(eds.),
4198:, 1996,
3985:See also
3554:locality
3499:Symmetry
3258:Atkinson
2719:coherent
2715:rational
2711:cardinal
2633:feasible
2622:and the
2129:Excluded
2120:Round 1
2063:Round 2
2060:Round 1
2009:ordering
1982:rational
1967:cardinal
1958:Cardinal
1899:function
1895:function
1880:ordering
1787:journals
1773:Glossary
1724:Stiglitz
1689:Rothbard
1669:Buchanan
1654:Friedman
1644:Koopmans
1634:Leontief
1614:Robinson
1499:Marshall
1403:Notable
1351:Regional
1327:Planning
1302:Monetary
1232:Feminist
1177:Cultural
1172:Business
977:a series
975:Part of
403:Hare STV
42:Politics
40:A joint
6132:Outline
6103:Schools
6095: (
6056:Piketty
6051:Krugman
5916:Kuznets
5906:Kalecki
5881:Polanyi
5771:Cournot
5766:Bastiat
5751:Ricardo
5741:Malthus
5731:Quesnay
5634:Marxian
5525:Chicago
5455:history
5450:Schools
5437:Welfare
5407:Service
5198:Applied
5032:Project
4723:D'Hondt
4675:CPO-STV
4633:Systems
4407:pp. 125
4362:pp. 771
3949:leximax
3947:is the
3850:leximin
3848:is the
3252:is the
2758:is the
2744:showing
2665:surface
2655:for an
2590:another
2537:Bentham
2381:scholar
2226:Please
2145:Bottom
2135:Center
2096:Bottom
2081:Center
2038:Example
2016:scoring
1951:ordinal
1942:Ordinal
1888:utility
1884:ranking
1793:Schools
1785: (
1744:Piketty
1739:Krugman
1604:Kuznets
1594:Kalecki
1569:Polanyi
1459:Cournot
1454:Bastiat
1439:Ricardo
1429:Malthus
1419:Quesnay
1391:Welfare
1361:Service
1032:Applied
1008:Outline
1003:History
413:CPO-STV
263:Baldwin
212:Schulze
207:Minimax
125:methods
6041:Thaler
6021:Ostrom
6016:Becker
6011:Sowell
5991:Baumol
5896:Myrdal
5891:Sraffa
5886:Frisch
5876:Knight
5871:Keynes
5846:Fisher
5841:Veblen
5826:Pareto
5806:Menger
5801:George
5796:Jevons
5791:Walras
5781:Gossen
5705:Thermo
5383:Public
5378:Policy
5333:Labour
5298:Health
5026:Portal
4963:Ballot
4739:Quotas
4468:series
4394:links.
4378:
4331:47–54.
4329:, pp.
4323:pp. 81
4311:
4249:
4233:", in
4206:
4172:
4141:
4093:
3671:where
3358:median
3354:person
3232:where
2926:among
2859:where
2445:. The
2383:
2376:
2369:
2362:
2354:
2002:choice
1897:—is a
1892:choice
1877:social
1729:Thaler
1709:Ostrom
1704:Becker
1699:Sowell
1679:Baumol
1584:Myrdal
1579:Sraffa
1574:Frisch
1564:Knight
1559:Keynes
1534:Fisher
1529:Veblen
1514:Pareto
1494:Menger
1489:George
1484:Jevons
1479:Walras
1469:Gossen
1337:Public
1332:Policy
1287:Labour
1252:Health
1109:Market
278:Coombs
48:series
6127:Lists
6122:Index
6073:Lists
6046:Hoppe
6031:Lucas
5996:Solow
5986:Arrow
5976:Simon
5941:Lange
5936:Hicks
5911:Röpke
5901:Hayek
5851:Pigou
5821:Clark
5736:Smith
5651:Mixed
5610:Post-
5432:Urban
5412:Socio
5402:Rural
4956:Other
4775:Mixed
4054:Notes
2388:JSTOR
2374:books
1890:, or
1766:Lists
1734:Hoppe
1719:Lucas
1684:Solow
1674:Arrow
1664:Simon
1629:Lange
1624:Hicks
1599:Röpke
1589:Hayek
1539:Pigou
1509:Clark
1424:Smith
1386:Urban
1366:Socio
1356:Rural
1056:Macro
1052:Micro
1013:Index
615:'MMP'
604:'AMS'
6062:more
5786:Marx
5776:Mill
5761:List
5639:Neo-
5595:Neo-
4464:and
4409:–39.
4376:ISBN
4364:–78.
4349:–46.
4309:ISBN
4247:ISBN
4204:ISBN
4170:ISBN
4139:ISBN
4091:ISBN
3888:For
3855:For
3533:are
3450:Euro
2791:The
2754:and
2638:sets
2598:1947
2549:1935
2360:news
2068:Top
1971:much
1961:(or
1945:(or
1871:, a
1867:and
1750:more
1474:Marx
1464:Mill
1449:List
556:Non-
510:SNTV
99:List
56:and
44:and
6026:Sen
5746:Say
5605:New
5338:Law
4788:MMP
3556:or
3540:4.
3517:3.
3496:2.
3479:1.
3051:min
2795:or
2717:or
2689:'s
2671:map
2602:any
2586:one
2535:of
2343:by
2230:to
2148:34
2102:47
2099:34
2071:40
1863:In
1714:Sen
1434:Say
1292:Law
274:el.
259:el.
248:IRV
244:el.
6158::
5029:—
4339:,
4237:;
4118:.
4114:.
3755::
3728:.
3537:.
3502::
3493:.
2770:A
2762:.
2559:.
2545:is
2195:.
2139:66
2125:—
2085:26
2075:53
2034:.
1988:.
1886:,
1882:,
1054:/
979:on
610:NZ
599:UK
175:US
164:UK
147:)
140:US
6099:)
5601:)
5597:(
5457:)
5453:(
5065:e
5058:t
5051:v
4443:e
4436:t
4429:v
4255:.
4210:.
4147:.
4120:4
4099:.
3902:1
3899:=
3869:0
3866:=
3792:1
3787:1
3773:1
3769:c
3749:w
3712:)
3709:u
3706:(
3703:w
3673:w
3656:)
3651:i
3647:u
3643:(
3640:w
3635:n
3630:1
3627:=
3624:i
3616:=
3613:)
3608:n
3604:u
3600:,
3594:,
3589:1
3585:u
3581:(
3578:W
3565:W
3549:R
3545:R
3531:v
3527:v
3523:v
3512:R
3508:R
3487:R
3470:R
3466:R
3429:T
3425:T
3416:e
3406:Y
3401:=
3395:T
3389:l
3386:i
3383:e
3380:h
3377:T
3372:W
3333:L
3329:T
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3310:Y
3305:=
3299:L
3293:l
3290:i
3287:e
3284:h
3281:T
3276:W
3240:G
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3217:G
3211:1
3208:(
3185:)
3182:G
3176:1
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3165:Y
3160:=
3154:i
3151:n
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3145:G
3140:W
3099:)
3094:n
3090:Y
3086:,
3080:,
3075:2
3071:Y
3067:,
3062:1
3058:Y
3054:(
3048:=
3045:W
3010:Y
3005:=
3000:i
2996:Y
2990:n
2985:1
2982:=
2979:i
2969:n
2966:1
2961:=
2958:W
2934:n
2914:i
2892:i
2888:Y
2867:W
2842:i
2838:Y
2832:n
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2821:i
2813:=
2810:W
2726:.
2694:(
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2469:(
2457:)
2453:(
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2378:·
2371:·
2364:·
2337:.
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2302:(
2297:)
2293:(
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2253:)
2247:(
2242:)
2238:(
2224:.
2202:)
2198:(
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1838:v
1789:)
961:e
954:t
947:v
612::
601::
280:)
271:(
265:)
256:(
250:)
241:(
177::
166::
142::
137:(
105:)
101:(
34:.
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