2070:
2290:. A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox for a total likelihood of 9.4%. While examples of the paradox seem to occur often in small settings like parliaments, very few examples have been found in larger groups (electorates), although some have been identified. However, the frequency of such paradoxes depends heavily on the number of options and other factors.
154:
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36:
2182:, according to which utility of an added quantity of a good decreases with the amount of the good that is already in possession of the individual. It has been used to defend transfers of wealth from the "rich" to the "poor" on the premise that the former do not derive as much utility as the latter from an extra unit of income. Robbins argued that this notion is beyond
81:
2621:
in the context of politics, is a rule that takes an individual's complete and transitive preferences over a set of outcomes and returns a single chosen outcome (or a set of tied outcomes). We can think of this subset as the winners of an election, and compare different social choice functions based
2023:
Because mechanism design places stronger assumptions on the behavior of voters or , it is sometimes possible to design mechanisms for social choice that accomplish "impossible" tasks. For example, by allowing agents to compensate each other for losses with transfers, the
2158:
have argued that preferences and utility functions of individuals are interpersonally comparable and may therefore be added together to arrive at a measure of aggregate utility. Utilitarian ethics call for maximizing this aggregate.
4580:
2126:
Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have
4625:
2020:, which is almost a reversal of Gibbard's theorem: for any given social choice function, there exists a mechanism that obtains the same results but incentivizes participants to be completely honest.
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3871:
2016:, a subset of social choice theory, deals with the identification of rules that preserve while incentivizing agents to honestly reveal their preferences. One particularly important result is the
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4249:
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2543:
2640:. That is, a voter may be able to cast a ballot that misrepresents their preferences to obtain a result that is more favorable to them under their sincere preferences.
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3078:
2439:
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2032:
outcome. As a result, the VCG mechanism can be considered a "better" way to make decisions than voting (though only so long as monetary transfers are possible).
1898:: Attempting to use majority rule as a social choice function creates situations where we have A better than B and B better than C, but C is also better than A.
2563:
2413:
2390:
2366:
2342:
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is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social choice functions. The
2227:
Despite the similar names, "public choice" and "social choice" are two distinct fields that are only weakly related. Public choice deals with the modeling of
4431:
1706:, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. The field is closely related to
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which are 'best' for society. The question of what 'best' means is a common question in social choice theory. The following rules are most common:
4392:
3579:
1976:
Gibbard's theorem provides limitations on the ability of any voting rule to elicit honest preferences from voters, showing that no voting rule is
1861:
3087:
2166:, questioned whether such measures of utility could be measured, or even considered meaningful. Following arguments similar to those espoused by
3217:
3196:
3614:
1905:, which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences are allowed.
2028:
can achieve the "impossible" according to
Gibbard's theorem: the mechanism ensures honest behavior from participants, while still achieving a
3993:
3792:
3744:
3657:
3599:
3564:
3537:
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2139:. But much of the research in the field assumes that those utility functions are internal to humans, lack a meaningful unit of measure and
2091:
4013:
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3408:
2179:
1785:
1923:
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2147:
is possible or not significantly alters the available mathematical structures for social welfare functions and social choice theory.
1971:
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that analyzes methods of combining individual opinions, beliefs, or preferences to reach a collective decision or create measures of
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3697:
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120:
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2674:
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1955:
1835:
1089:
4719:
4173:
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1004:
2266:(with Clubs, Committees, and Associations) whereas Public Choice falls under JEL D72 (Economic Models of Political Processes:
4729:
4100:
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2587:
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1104:
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argues that even if interpersonal comparisons of utility are imperfect, we can still say that (despite being positive for
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604:
342:
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1789:
is often recognized as inaugurating the modern era of social choice theory. Later work has also considered approaches to
51:
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1242:
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https://www.jstor.org/discover/10.2307/4092266?uid=3739936&uid=2&uid=4&uid=3739256&sid=21102056001967
3422:
_____, (1972). "General
Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice", Nobel Prize Lecture,
2235:(predicting how politicians and other stakeholders will act). It is therefore often thought of as the application of
2084:
2078:
1750:
98:
91:
3135: Charles Blackorby, Walter Bossert, and David Donaldson, 2002. "Utilitarianism and the Theory of Justice", in
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4663:
4127:
3736:
2653:
2049:
2041:
1810:
1079:
1050:
997:
947:
477:
467:
3319:
Kurrild-Klitgaard, Peter (2014). "An empirical example of the
Condorcet paradox of voting in a large electorate".
4699:
4523:
4456:
4451:
4414:
3945:
3918:
3888:
3540:
2842:
Zwicker, William S.; Moulin, Herve (2016), Brandt, Felix; Conitzer, Vincent; Endriss, Ulle; Lang, Jerome (eds.),
2657:
2053:
1601:
1206:
357:
56:
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4244:
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2263:
2255:
1321:
1211:
926:
664:
619:
472:
241:
185:
2892:, Advances in Group Decision and Negotiation, vol. 5, Dordrecht: Springer Netherlands, pp. 101–123,
679:
2186:; that is, one cannot measure changes in the utility of someone else, nor is it required by positive theory.
1868:
the system can behave erratically in response to changes in the quality or popularity of one of the options.
4569:
2299:
2045:
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1251:
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427:
387:
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be a set of possible 'states of the world' or 'alternatives'. Society wishes to choose a single state from
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4345:
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agreed that perfect comparisons of mental states are not practically possible, but people can still make
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2213:
comparability of utility is possible, and social choice theory should proceed under that assumption.
2017:
1996:
1967:
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4156:
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3552:
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2286:, but some research has aimed at estimating the frequency of various voting paradoxes, such as the
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2189:
Apologists for the interpersonal comparison of utility have argued that
Robbins claimed too much.
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536:
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511:
462:
402:
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337:
332:
304:
299:
269:
137:
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and
Christian List (2003). "Social Choice Theory and Deliberative Democracy: A Reconciliation,"
3127:
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4195:
4122:
4083:
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3766:
3740:
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3560:
3533:
3525:
3460:
3452:
3438:
3413:
3336:
3293:
3247:
3165:
3139:, edited by Kenneth J. Arrow, Amartya K. Sen, and Kotaro Suzumura, v. 1, ch. 11, pp. 543–596.
3054:
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3013:
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2013:
2007:
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1707:
1513:
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implies that the only rule satisfying non-imposition (every alternative can be chosen) and
1980:(i.e. does not depend on other voters' preferences) for elections with 3 or more outcomes.
1894:
when three or more options are available. Majority rule can create cycles that violate the
153:
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4232:
4227:
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492:
264:
259:
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comparisons thanks to their similar backgrounds, cultural experiences, and psychologies.
1987:, showing that no such voting rule can be sincere (i.e. free of reversed preferences).
1679:
to find the best ways to combine individual preferences into a coherent whole, called a
4149:
3781:
3776:
3666:
3545:
3515:
3364:"A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision"
3112: ch. 9*, "Impersonality and Collective Quasi-Orderings," pp. 152-160.
2548:
2398:
2375:
2351:
2327:
2307:
2259:
2236:
2163:
2155:
2151:
1865:
1802:
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1342:
1284:
904:
889:
854:
839:
819:
789:
639:
609:
526:
216:
212:
102:
3827:
3161:
3050:
3017:
2791:
2787:
2251:
bent, and deals with the abstract study of decision procedures and their properties.
1586:
4678:
4466:
4421:
4404:
4050:
3923:
3849:
3609:
3573:
3403:
3348:
3305:
3259:
2739:
2618:
2222:
2190:
2175:
1984:
1919:
1887:
1794:
1780:
1758:
1393:
1371:
1346:
1176:
869:
859:
834:
774:
769:
764:
744:
734:
704:
694:
599:
502:
3810:
3700:
3105:
4486:
4365:
4144:
4055:
3950:
3587:
2267:
1699:
1156:
985:
899:
844:
739:
729:
724:
649:
197:
3123:
2927:
2855:
2805:
4597:
4513:
3685:
3491:
Bossert, Walter and John A. Weymark (2008). "Social Choice (New
Developments),"
3276:
Van Deemen, Adrian (2014). "On the empirical relevance of
Condorcet's paradox".
2897:
2763:
2699:
2283:
2279:
2278:
Since Arrow, social choice theory has been characterized by being predominantly
2198:
2167:
1947:
1762:
1719:
1676:
1664:
1460:
1425:
1328:
1316:
1181:
874:
864:
654:
289:
97:
The references used may be made clearer with a different or consistent style of
2991:
Walter
Bossert and John A. Weymark (2008). "Social Choice (New Developments),"
4533:
3752:
3332:
3289:
3243:
2970:
2885:
2579:
2244:
2183:
2128:
1818:
1668:
1550:
1540:
1535:
1274:
1136:
784:
584:
3751:. A comprehensive reference from a computational perspective; see Chapter 9.
3340:
3297:
3251:
3230:
Kurrild-Klitgaard, Peter (2014). "Empirical social choice: An introduction".
2978:
17:
3896:
2954:
1883:
1660:
1435:
1333:
1216:
1171:
1151:
634:
565:
145:
1922:'s utilitarian theorem shows that if individuals have preferences that are
3091: Louis Kaplow (2008). "Pareto Principle and Competing Principles,"
968:
3637:
2597:
1745:
The earliest work on social choice theory comes from the writings of the
1558:
1518:
1201:
1186:
1166:
1035:
3732:
Multiagent
Systems: Algorithmic, Game-Theoretic, and Logical Foundations
3156:. Handbook of Social Choice and Welfare. Vol. 1. pp. 597–633.
3045:. Handbook of Social Choice and Welfare. Vol. 1. pp. 459–541.
3012:. Handbook of Social Choice and Welfare. Vol. 2. pp. 153–187.
2209:
had a negative overall value. Harsanyi and Sen thus argue that at least
3705:
_____, (1998). "The
Possibility of Social Choice", Nobel Prize Lecture
3387:
3363:
2484:
2171:
1951:
1891:
1715:
1473:
1131:
2231:
as they actually exist in the real world, and is primarily limited to
4581:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
4200:
4018:
3447:
Arrow, Kenneth J., Amartya K. Sen, and Kotaro Suzumura, eds. (1997).
3043:
Chapter 10 Social welfare functionals and interpersonal comparability
1703:
1691:
1523:
1465:
1363:
3379:
2821:
2415:
be a finite set, representing a collection of individuals. For each
3839:
2040:
If the domain of preferences is restricted to those that include a
43:
It has been suggested that some portions of this article should be
1773:), which discussed many of the same concepts, but was lost in the
3678:
____, (1938). "Interpersonal Comparisons of Utility: A Comment,"
3843:
3730:
2202:
4636:
European Community on Computational Methods in Applied Sciences
3853:
2143:
be compared across different individuals. Whether this type of
1983:
The Gibbard–Satterthwaite theorem proves a stronger result for
3082: Bertil Tungodden (2008). "Justice (New Perspectives),"
2884:
Nurmi, Hannu (2010), Rios Insua, David; French, Simon (eds.),
2063:
74:
29:
3548:(1996). Théories économiques de la justice, Paris: Economica.
4631:
International Council for Industrial and Applied Mathematics
2955:"Ramon Llull: from 'Ars electionis' to social choice theory"
2790:, section 2, A Notation for Preferences and Choice, and ch.
1946:, who identified democracy with the ideal of maximizing the
3672:
An Essay on the Nature and Significance of Economic Science
3210:
An Essay on the Nature and Significance of Economic Science
3189:
An Essay on the Nature and Significance of Economic Science
3110: ch. 9, "Equity and Justice," pp. 131-51.
1840:
Arrow's impossibility theorem is a key result showing that
1710:, which can be thought of as modelling social choice with
1659:
make decisions). Social choice incorporates insights from
3846:
covering many subjects of social choice and voting theory
3763:
Rational Choice, Collective Decisions, and Social Welfare
2890:
e-Democracy: A Group Decision and Negotiation Perspective
2850:, Cambridge: Cambridge University Press, pp. 23–56,
2622:
on which axioms or mathematical properties they fulfill.
2162:
In contrast many twentieth century economists, following
1942:. This lends some support to the viewpoint expressed of
4250:
Numerical methods for ordinary differential equations
3612:(June 2013). "Fundamentals of social choice theory".
2551:
2505:
2447:
2421:
2401:
2378:
2354:
2330:
2310:
4626:
Société de Mathématiques Appliquées et Industrielles
4619:
Japan Society for Industrial and Applied Mathematics
4255:
Numerical methods for partial differential equations
1698:. Real-world examples include enacting laws under a
4606:
4590:
4552:
4504:
4442:
4317:
4275:
4069:
4031:
3969:
3887:
2488:, describing the amount of happiness an individual
2475:{\displaystyle u_{i}:X\longrightarrow \mathbb {R} }
2256:
Journal of Economic Literature classification codes
1749:, who formulated several key results including his
3780:
2644:shows that when there are only two candidates and
2557:
2537:
2474:
2433:
2407:
2384:
2360:
2336:
2316:
3783:Social choice and the mathematics of manipulation
2270:, Elections, Legislatures, and Voting Behavior).
1886:cannot be thought of as being the same as simple
1777:and only rediscovered in the early 21st century.
2131:, and it follows that they can be modeled using
2636:when there are more than two candidates is the
4614:Society for Industrial and Applied Mathematics
3520:Feldman, Allan M. and Roberto Serrano (2006).
3426:, with Section 8 on the theory and background.
1718:citizens; it thus involves the application of
3865:
3652:. Cambridge, UK: Cambridge University Press.
3576:(1987). "Interpersonal Utility Comparisons,"
3484:, v. 2, Amsterdam: Elsevier. Chapter-preview
2617:A social choice function, sometimes called a
2247:. By contrast, social choice has a much more
1651:make decisions, whereas political science is
1609:
1005:
8:
4432:Supersymmetric theory of stochastic dynamics
3008:Kaushik, Basu; Lòpez-Calva, Luis F. (2011).
3713:The New Palgrave: A Dictionary of Economics
3041:d'Aspremont, Claude; Gevers, Louis (2002).
2044:, then selecting that winner is the unique
4439:
3966:
3872:
3858:
3850:
3729:Shoham, Yoav; Leyton-Brown, Kevin (2009).
3715:, v. 4, London: Palgrave, pp. 382–93.
3583:, v. 2, London: Palgrave, pp. 955–58.
3522:Welfare Economics and Social Choice Theory
3497:, 2nd Edition, London: Palgrave Macmillan
3183:
3181:
3154:Chapter 12 Inequality, poverty and welfare
2368:may represent the set of candidates; in a
1890:or majoritarianism; otherwise, it will be
1616:
1602:
1023:
1012:
998:
132:
3828:Social Choice Bibliography by J. S. Kelly
3627:
3594:. Cambridge: Cambridge University Press.
3084:The New Palgrave Dictionary of Economics,
3075:The New Palgrave Dictionary of Economics,
2782:For example, in Kenneth J. Arrow (1951).
2759:
2757:
2755:
2550:
2523:
2513:
2504:
2468:
2467:
2452:
2446:
2420:
2400:
2377:
2353:
2329:
2309:
2114:Learn how and when to remove this message
1729:in that the latter is concerned with how
1694:, social choice is sometimes also called
121:Learn how and when to remove this message
3787:. New York: Cambridge University Press.
3765:, Cambridge: Cambridge University Press
3720:The New Palgrave Dictionary of Economics
3494:The New Palgrave Dictionary of Economics
3093:The New Palgrave Dictionary of Economics
2993:The New Palgrave Dictionary of Economics
2768:The New Palgrave Dictionary of Economics
2602:– aims to maximize the smallest utility.
2584:– aims to maximize the sum of utilities.
2392:may represent all possible allocations.
2077:This section includes a list of general
1815:capabilities and functionings approaches
3580:New Palgrave: A Dictionary of Economics
3208:Lionel Robbins (1932, 1935, 2nd ed.).
3187:Lionel Robbins (1932, 1935, 2nd ed.).
2848:Handbook of Computational Social Choice
2751:
1862:independence of irrelevant alternatives
1034:
144:
3615:Quarterly Journal of Political Science
2844:"Introduction to the Theory of Voting"
2646:only rankings of options are available
2243:, in order to predict the behavior of
1882:Condorcet's example demonstrates that
3592:Axioms of cooperative decision making
3482:Handbook of Social Choice and Welfare
3471:Handbook of Social Choice and Welfare
3451:, 2 vol., London: Palgrave Macmillan
3271:
3269:
3137:Handbook of Social Choice and Welfare
2026:Vickrey–Clarke–Groves (VCG) mechanism
1829:
1686:Because of its strong connections to
7:
3690:Collective Choice and Social Welfare
3675:, 2nd ed., London: Macmillan, ch. VI
3508:British Journal of Political Science
3102:Collective Choice and Social Welfare
2837:
2835:
2833:
2831:
2217:Relationship to public choice theory
3820:Stanford Encyclopedia of Philosophy
3559:. Oxford: Oxford University Press.
3409:Social Choice and Individual Values
2784:Social Choice and Individual Values
2499:is a mechanism which uses the data
2180:law of diminishing marginal utility
2056:, and non-manipulable voting rule.
1786:Social Choice and Individual Values
52:interpersonal comparison of utility
3881:Industrial and applied mathematics
3541:Arrow-searchable chapter previews.
2492:derives from each possible state.
2083:it lacks sufficient corresponding
2042:majority-strength Condorcet winner
1954:) of society as a whole, under an
25:
4111:Stochastic differential equations
3718:_____, (2008). "Social Choice,".
3122:, Cambridge, MA: Belknap Press,
2926:Coughlin, Peter J. (1992-10-30).
1647:field that studies how societies
1484:Biology and political orientation
4427:Supersymmetric quantum mechanics
3722:, 2nd Edition, London: Palgrave
3711:_____, (1987). "Social Choice,"
3650:Collective Preference and Choice
3557:A primer in social choice theory
3362:May, Kenneth O. (October 1952).
3114: Kenneth J. Arrow (1983).
3073:Amartya Sen ( 2008). "Justice,"
2953:Colomer, Josep M. (2013-02-01).
2794:, "The Social Welfare Function".
2538:{\displaystyle (u_{i})_{i\in I}}
2145:interpersonal utility comparison
2068:
2060:Interpersonal utility comparison
1956:equal consideration of interests
1585:
979:
967:
152:
79:
34:
4309:Stochastic variational calculus
4101:Ordinary differential equations
3212:, London: Macmillan. Links for
3191:, London: Macmillan. Links for
3100: Amartya K. Sen (1979 ).
2545:to select some element(s) from
1737:, can make rational decisions.
254:Concepts, theory and techniques
4106:Partial differential equations
3979:Arbitrary-precision arithmetic
3524:, 2nd ed., New York: Springer
2932:. Cambridge University Press.
2520:
2506:
2464:
2150:In one perspective, following
1938:social choice function is the
1924:well-behaved under uncertainty
1915:Harsanyi's utilitarian theorem
1479:Theories of political behavior
1105:Political history of the world
1:
3994:Interactive geometry software
3162:10.1016/S1574-0110(02)80016-9
3051:10.1016/S1574-0110(02)80014-5
3018:10.1016/S0169-7218(10)00016-X
3010:Functionings and Capabilities
2675:Arrow's impossibility theorem
2630:Gibbard–Satterthwaite theorem
2626:Arrow's impossibility theorem
2170:, Robbins argued concepts of
1972:Gibbard–Satterthwaite theorem
1836:Arrow's impossibility theorem
1830:Arrow's impossibility theorem
1761:. His work was prefigured by
1757:showing the impossibility of
1494:Critique of political economy
2856:10.1017/cbo9781107446984.003
2735:Rule according to higher law
2178:. Consider for instance the
1985:ranked-choice voting systems
1075:Outline of political science
4046:Computational number theory
4009:Numerical-analysis software
2929:Probabilistic Voting Theory
2898:10.1007/978-90-481-9045-4_7
2804:Fishburn, Peter C. (1974).
2685:Computational social choice
1725:Social choice differs from
4746:
3737:Cambridge University Press
2766:(2008). "Social Choice,".
2610:
2297:
2258:place Social Choice under
2220:
2168:behaviorists in psychology
2005:
1994:
1965:
1912:
1875:
1833:
1080:Index of politics articles
49:into a new article titled
4644:
4452:Algebra of physical space
3919:Automated theorem proving
3449:Social Choice Re-Examined
3435:Social Choice and Justice
3290:10.1007/s11127-013-0133-3
3244:10.1007/s11127-014-0164-4
3120:Social Choice and Justice
2971:10.1007/s00355-011-0598-2
2959:Social Choice and Welfare
2806:"Social Choice Functions"
1655:(observing how societies
4245:Numerical linear algebra
3753:Downloadable free online
3510:, 33(1), pp. 1–28,
3473:, v. 1. Chapter-preview
1864:, i.e. they suffer from
1860:). Such systems violate
242:JEL classification codes
4710:Collective intelligence
3984:Finite element analysis
3934:Constraint satisfaction
3406:(1951, 2nd ed., 1963).
3333:10.1023/A:1010304729545
3152:Dutta, Bhaskar (2002).
2786:, New York: Wiley, ch.
2607:Social choice functions
2592:– sometimes called the
2574:– sometimes called the
2300:Social welfare function
2098:more precise citations.
1908:
1842:social choice functions
1681:social welfare function
1489:Political organisations
1252:International relations
1090:Politics by subdivision
428:Industrial organization
285:Computational economics
4720:Mathematical economics
4539:Mathematical economics
4213:Multivariable calculus
4096:Differential equations
3939:Constraint programming
3929:Computational geometry
3811:"Social Choice Theory"
3130:, and chapter-preview
3104:, New York: Elsevier,
2730:Rational choice theory
2680:Compensation principle
2638:dictatorship mechanism
2613:Social choice function
2559:
2539:
2476:
2435:
2434:{\displaystyle i\in I}
2409:
2386:
2362:
2346:single-winner election
2338:
2318:
2174:were unscientific and
280:Experimental economics
4730:Administrative theory
4492:Supersymmetry algebra
4477:Representation theory
4472:Renormalization group
4118:Differential geometry
3999:Optimization software
3971:Mathematical software
3692:, New York: Elsevier
2705:Group decision-making
2662:positively-responsive
2560:
2540:
2477:
2436:
2410:
2387:
2363:
2339:
2319:
1962:Manipulation theorems
1569:Political campaigning
1309:Public administration
1142:Collective leadership
4715:Political philosophy
4685:Social choice theory
4544:Mathematical finance
4529:Social choice theory
4444:Algebraic structures
4393:in quantum mechanics
4329:Analytical mechanics
4295:Stochastic processes
4267:Variational calculus
4079:Approximation theory
4004:Statistical software
3638:10.1561/100.00013006
3469:_____, eds. (2002).
3437:, Oxford: Blackwell
2650:simple majority vote
2549:
2503:
2445:
2419:
2399:
2376:
2352:
2344:. For example, in a
2328:
2308:
2018:revelation principle
1997:Median voter theorem
1991:Median voter theorem
1901:This contrasts with
1799:variable populations
1771:The Art of Elections
1747:Marquis de Condorcet
1688:political philosophy
1639:. It contrasts with
1629:Social choice theory
1419:Separation of powers
1290:Political psychology
1265:Comparative politics
1243:political scientists
1230:Academic disciplines
1110:Political philosophy
507:Social choice theory
4705:Applied mathematics
4519:Operations research
4388:Perturbation theory
4186:Multilinear algebra
4157:Functional analysis
4014:Numerical libraries
3946:Computational logic
3480:_____, ed. (2011).
3412:, New York: Wiley.
3079:Abstract & TOC.
2997:Abstract & TOC.
2772:Abstract & TOC.
2710:Justice (economics)
2370:resource allocation
1896:transitive property
1846:ordinal comparisons
1819:measures of welfare
1765:'s 1299 manuscript
1592:Politics portal
1441:Election commission
1412:Government branches
1295:Political sociology
1147:Confessional system
1085:Politics by country
974:Business portal
295:Operations research
275:National accounting
27:Academic discipline
4656:Mathematics portal
4553:Other applications
4277:Probability theory
4260:Validated numerics
4240:Numerical analysis
4133:Geometric analysis
4123:Differential forms
3956:Information theory
3833:2017-12-23 at the
2581:Benthamite welfare
2555:
2535:
2497:social choice rule
2472:
2431:
2405:
2382:
2358:
2334:
2314:
2274:Empirical research
2233:positive economics
2207:Great Fire of Rome
1909:Harsanyi's theorem
1892:self-contradictory
1791:legal compensation
1275:Political analysis
1207:Semi-parliamentary
305:Industrial complex
300:Middle income trap
4725:Law and economics
4695:Political science
4672:
4671:
4506:Decision sciences
4500:
4499:
4482:Spacetime algebra
4174:Harmonic analysis
4140:Dynamical systems
4084:Clifford analysis
4061:Discrete geometry
4027:
4026:
3809:List, Christian.
3794:978-0-521-00883-9
3746:978-0-521-89943-7
3659:978-0-521-72213-1
3610:Myerson, Roger B.
3601:978-0-521-42458-5
3574:Harsanyi, John C.
3566:978-0-19-929751-1
3538:978-0-387-29367-7
3404:Arrow, Kenneth J.
2939:978-0-521-36052-4
2907:978-90-481-9045-4
2865:978-1-107-44698-4
2695:Extended sympathy
2690:Condorcet paradox
2634:strategyproofness
2558:{\displaystyle X}
2408:{\displaystyle I}
2385:{\displaystyle X}
2361:{\displaystyle X}
2337:{\displaystyle X}
2317:{\displaystyle X}
2288:Condorcet paradox
2241:political science
2229:political systems
2133:utility functions
2124:
2123:
2116:
1968:Gibbard's theorem
1856:(unless they are
1811:natural resources
1805:of social-choice
1803:strategy-proofing
1673:political science
1641:political science
1637:social well-being
1633:welfare economics
1626:
1625:
1574:Political parties
1514:Electoral systems
1238:Political science
1212:Semi-presidential
1124:Political systems
1100:Political history
1095:Political economy
1022:
1021:
131:
130:
123:
73:
72:
16:(Redirected from
4737:
4700:Public economics
4457:Feynman integral
4440:
4400:Potential theory
4289:random variables
4179:Fourier analysis
4162:Operator algebra
4089:Clifford algebra
4041:Computer algebra
3967:
3874:
3867:
3860:
3851:
3824:
3815:Zalta, Edward N.
3798:
3786:
3759:Suzumura, Kotaro
3750:
3682:, 43(4), 635–41.
3680:Economic Journal
3663:
3641:
3631:
3605:
3570:
3431:Collected Papers
3392:
3391:
3359:
3353:
3352:
3327:(1/2): 135–145.
3316:
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3309:
3284:(3–4): 311–330.
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3238:(3–4): 297–310.
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3116:Collected Papers
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2720:Mechanism design
2599:Rawlsian welfare
2589:Egalitarian rule
2571:Utilitarian rule
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2245:political actors
2184:positive science
2119:
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2108:
2105:
2099:
2094:this section by
2085:inline citations
2072:
2071:
2064:
2030:Pareto efficient
2014:mechanism design
2008:Mechanism design
2002:Mechanism design
1944:John Stuart Mill
1940:utilitarian rule
1936:Pareto efficient
1872:Condorcet cycles
1850:cardinal utility
1775:Late Middle Ages
1714:and potentially
1708:mechanism design
1643:in that it is a
1618:
1611:
1604:
1590:
1589:
1380:
1325:
1280:Political theory
1270:Election science
1260:
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1024:
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986:Money portal
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468:Natural resource
260:Economic systems
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4462:Poisson algebra
4438:
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4167:Operator theory
4065:
4023:
3989:Tensor software
3965:
3914:Automata theory
3883:
3878:
3835:Wayback Machine
3808:
3805:
3795:
3777:Taylor, Alan D.
3775:
3747:
3728:
3686:Sen, Amartya K.
3667:Robbins, Lionel
3660:
3644:
3629:10.1.1.297.6781
3608:
3602:
3586:
3567:
3551:
3546:Fleurbaey, Marc
3504:Dryzek, John S.
3429:_____, (1983).
3400:
3395:
3380:10.2307/1907651
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3095:, 2nd Edition.
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2995:, 2nd Edition,
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2886:"Voting Theory"
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2822:10.1137/1016005
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2770:, 2nd Edition,
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2715:Liberal paradox
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1966:Main articles:
1964:
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1878:Condorcet cycle
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1866:spoiler effects
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1727:decision theory
1712:self-interested
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3622:(3): 305–337.
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3553:Gaertner, Wulf
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1844:based only on
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4422:Supersymmetry
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4405:String theory
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4304:Path integral
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4285:Distributions
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3924:Coding theory
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3321:Public Choice
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3106:(description)
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2664:voting rule.
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2659:
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2647:
2643:
2642:May's theorem
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2237:microeconomic
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2223:Public choice
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2208:
2204:
2200:
2196:
2192:
2191:John Harsanyi
2187:
2185:
2181:
2177:
2176:unfalsifiable
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2021:
2019:
2015:
2012:The field of
2009:
2001:
1998:
1990:
1988:
1986:
1981:
1979:
1978:strategyproof
1973:
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1953:
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1937:
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1929:
1925:
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1916:
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1903:May's theorem
1899:
1897:
1893:
1889:
1888:majority rule
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1796:
1795:fair division
1792:
1788:
1787:
1782:
1781:Kenneth Arrow
1778:
1776:
1772:
1768:
1764:
1760:
1759:majority rule
1756:
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1696:voting theory
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1400:
1397:
1395:
1394:Civil society
1392:
1390:
1387:
1385:
1382:
1378:
1373:
1372:Public policy
1370:
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1234:
1226:
1225:
1218:
1215:
1213:
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1192:Parliamentary
1190:
1188:
1185:
1183:
1180:
1178:
1177:Hybrid regime
1175:
1173:
1170:
1168:
1165:
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1148:
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1125:
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711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
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678:
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663:
661:
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653:
651:
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608:
606:
603:
601:
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596:
593:
591:
588:
586:
583:
581:
578:
576:
575:de Mandeville
573:
572:
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560:
553:
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540:
538:
535:
533:
530:
528:
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520:
518:
515:
513:
510:
508:
504:
503:Public choice
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
478:Participation
476:
474:
471:
469:
466:
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461:
459:
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454:
451:
449:
446:
444:
441:
439:
438:Institutional
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421:
419:
416:
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409:
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404:
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388:Expeditionary
386:
384:
381:
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378:Environmental
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208:International
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184:Branches and
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88:This article
86:
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53:
48:
47:
41:
32:
31:
19:
18:Social Choice
4662: /
4658: /
4648:
4528:
4524:Optimization
4487:Superalgebra
4346:Field theory
4319:Mathematical
4297: /
4145:Chaos theory
4128:Gauge theory
4056:Graph theory
3951:Cryptography
3818:
3782:
3762:
3735:. New York:
3731:
3719:
3712:
3701:Description.
3689:
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3492:
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3424:Link to text
3407:
3371:
3368:Econometrica
3367:
3357:
3324:
3320:
3314:
3281:
3277:
3235:
3231:
3225:
3209:
3204:
3188:
3153:
3147:
3136:
3119:
3115:
3101:
3092:
3083:
3074:
3069:
3042:
3036:
3009:
3003:
2992:
2987:
2962:
2958:
2948:
2928:
2921:
2911:, retrieved
2889:
2879:
2869:, retrieved
2847:
2813:
2809:
2799:
2783:
2778:
2767:
2624:
2616:
2598:
2594:max-min rule
2593:
2588:
2580:
2576:max-sum rule
2575:
2570:
2496:
2494:
2489:
2483:
2394:
2303:
2280:mathematical
2277:
2268:Rent-Seeking
2253:
2226:
2210:
2194:
2188:
2161:
2156:utilitarians
2149:
2144:
2140:
2125:
2110:
2101:
2082:
2039:
2022:
2011:
1982:
1975:
1930:), the only
1918:
1900:
1881:
1854:incoherently
1839:
1784:
1779:
1770:
1766:
1751:jury theorem
1744:
1734:
1730:
1724:
1700:constitution
1695:
1685:
1656:
1648:
1628:
1627:
1322:street-level
1197:Presidential
1157:Dictatorship
1027:Part of the
944:Publications
909:
532:Sociological
506:
505: /
403:Geographical
383:Evolutionary
358:Digitization
323:Agricultural
227:Mathematical
198:Econometrics
117:
108:
89:
61:
50:
44:
4664:topics list
4598:Mathematics
4514:Game theory
4415:Topological
4381:Topological
4376:Statistical
4339:Hamiltonian
3514:, 2002 PDF
3124:Description
2810:SIAM Review
2764:Amartya Sen
2700:Game theory
2284:theoretical
2199:Amartya Sen
2137:VNM theorem
2129:preferences
2096:introducing
1948:common good
1858:dictatorial
1825:Key results
1763:Ramon Llull
1755:his example
1731:individuals
1720:game theory
1677:game theory
1665:mathematics
1653:descriptive
1461:Sovereignty
1426:Legislature
1329:Technocracy
1317:Bureaucracy
1182:Meritocracy
1162:Directorial
780:von Neumann
433:Information
373:Engineering
353:Development
348:Demographic
290:Game theory
232:Methodology
4690:Metaethics
4679:Categories
4570:Psychology
4534:Statistics
4334:Lagrangian
3961:Statistics
3897:Algorithms
3840:Electowiki
3398:References
2913:2024-06-20
2871:2021-12-24
2239:models to
2221:See also:
2079:references
2046:resolvable
1807:mechanisms
1801:, partial
1669:philosophy
1551:Governance
1541:Government
1536:Federalism
1137:City-state
939:Economists
810:Schumacher
715:Schumpeter
685:von Wieser
605:von ThĂĽnen
566:economists
542:Statistics
537:Solidarity
458:Managerial
423:Humanistic
418:Historical
363:Ecological
328:Behavioral
222:Mainstream
111:April 2021
103:footnoting
4575:Sociology
4565:Chemistry
4361:Effective
4356:Conformal
4351:Classical
4223:Geometric
4196:Geometric
3724:Abstract.
3688:(1970 ).
3624:CiteSeerX
3499:Abstract.
3349:152300013
3341:0048-5829
3306:154862595
3298:0048-5829
3260:148982833
3252:0048-5829
3214:1932 HTML
3193:1932 HTML
3141:Abstract.
3097:Abstract.
3088:Abstract.
2979:1432-217X
2816:: 63–90.
2658:anonymous
2528:∈
2465:⟶
2426:∈
2372:setting,
2249:normative
2135:, by the
2054:anonymous
1884:democracy
1735:societies
1716:dishonest
1661:economics
1645:normative
1531:Unitarism
1519:Elections
1507:Subseries
1436:Judiciary
1431:Executive
1334:Adhocracy
1217:Theocracy
1172:Feudalism
1152:Democracy
855:Greenspan
820:Samuelson
800:Galbraith
770:Tinbergen
710:von Mises
705:Heckscher
665:Edgeworth
483:Personnel
443:Knowledge
408:Happiness
398:Financial
368:Education
343:Democracy
237:Political
203:Heterodox
146:Economics
4650:Category
4299:analysis
4218:Exterior
4191:Exterior
4071:Analysis
4033:Discrete
3907:analysis
3831:Archived
3779:(2005).
3761:(1983).
3669:(1935).
3648:(2010).
3590:(1988).
3555:(2006).
3433:, v. 1,
3128:contents
3118:, v. 1,
2668:See also
2104:May 2024
1932:coherent
1928:coherent
1920:Harsanyi
1783:'s book
1559:Ideology
1377:doctrine
1338:Service
1202:Republic
1187:Monarchy
1167:Federacy
1056:Category
1036:Politics
948:journals
934:Glossary
885:Stiglitz
850:Rothbard
830:Buchanan
815:Friedman
805:Koopmans
795:Leontief
775:Robinson
660:Marshall
564:Notable
512:Regional
488:Planning
463:Monetary
393:Feminist
338:Cultural
333:Business
138:a series
136:Part of
99:citation
64:May 2024
4660:outline
4591:Related
4560:Biology
4410:Bosonic
4371:Quantum
4321:physics
4287: (
4019:Solvers
3817:(ed.).
3388:1907651
2654:neutral
2264:JEL D71
2211:partial
2172:utility
2092:improve
2050:neutral
1952:utility
1741:History
1564:Culture
1474:Country
1132:Anarchy
1046:Outline
954:Schools
946: (
905:Piketty
900:Krugman
765:Kuznets
755:Kalecki
730:Polanyi
620:Cournot
615:Bastiat
600:Ricardo
590:Malthus
580:Quesnay
552:Welfare
522:Service
193:Applied
169:Outline
164:History
57:discuss
4233:Vector
4228:Tensor
4206:Vector
4201:Tensor
3902:design
3791:
3769:
3743:
3696:
3656:
3626:
3598:
3563:
3536:
3528:
3463:
3459:&
3455:
3441:
3416:
3386:
3347:
3339:
3304:
3296:
3258:
3250:
3168:
3132:links.
3057:
3024:
2977:
2936:
2904:
2862:
2660:, and
2648:, the
2441:, let
2205:) the
2141:cannot
2081:, but
2036:Others
1926:(i.e.
1817:, and
1704:voting
1692:voting
1675:, and
1649:should
1524:voting
1466:Polity
1364:Policy
1343:Public
1257:theory
890:Thaler
870:Ostrom
865:Becker
860:Sowell
840:Baumol
745:Myrdal
740:Sraffa
735:Frisch
725:Knight
720:Keynes
695:Fisher
690:Veblen
675:Pareto
655:Menger
650:George
645:Jevons
640:Walras
630:Gossen
498:Public
493:Policy
448:Labour
413:Health
270:Market
4366:Gauge
3813:. In
3516:link.
3486:links
3475:links
3384:JSTOR
3345:S2CID
3302:S2CID
3256:S2CID
2747:Notes
2482:be a
2294:Rules
1547:forms
1470:State
1347:Civil
1051:Index
927:Lists
895:Hoppe
880:Lucas
845:Solow
835:Arrow
825:Simon
790:Lange
785:Hicks
760:Röpke
750:Hayek
700:Pigou
670:Clark
585:Smith
547:Urban
527:Socio
517:Rural
217:Macro
213:Micro
174:Index
46:split
3844:wiki
3842:, a
3789:ISBN
3767:ISBN
3741:ISBN
3694:ISBN
3654:ISBN
3596:ISBN
3578:The
3561:ISBN
3534:ISBN
3526:ISBN
3461:ISBN
3453:ISBN
3439:ISBN
3414:ISBN
3337:ISSN
3294:ISSN
3248:ISSN
3216:and
3195:and
3166:ISBN
3055:ISBN
3022:ISBN
2975:ISSN
2934:ISBN
2902:ISBN
2860:ISBN
2395:Let
2304:Let
2282:and
2254:The
2203:Nero
2195:some
1970:and
1950:(or
1934:and
1753:and
1690:and
911:more
635:Marx
625:Mill
610:List
101:and
3634:doi
3376:doi
3329:doi
3325:107
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3282:158
3240:doi
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3158:doi
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875:Sen
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