Thursday, July 29, 2010

Advantages and Disadvantages of Majority Vote and Super Majorities, thoughtful Thursday

  1. James M. Buchanan and Gordon Tullock, The Calculus of Consent Ann Arbor Paperbacks
  2. Kenneth O. May, "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision" Econometrica Volume Twenty, Number Four, October 1952 , pages 680 to 684.
  3. Dean Lacy and Emerson M. S. Niou, "A Problem with Referendums" May Tenth 1998. (online, but appears to be a copy of "A Problem with Referencums" Journal of Theoretical Politics 12 (1, January) 5,31.
  4. Hannu Nurmi, "Referendum Design: An Exercise in Applied Social Choice" Scandinavian Political Studies Volume Twenty Number One 1997.
  5. Anthony McGainn, the Tyranny of the Super Majoirty: Howe Majority Rule Protects Minorities

Majority Rule--all decisions should require 50% + one to pass, whether it is an election, in a legislature or on a referendum. Dr. Buchanan says that in an ideal world, if we could only overcome the costs of reaching a decision, we should require unanimity. Assuming that person X is voting on the referendum to select a constitution. He should want one where decisions must be unanimous. He would never be taxed for programs he did not like. He would never be required to obey regulations, say to limit his use of the land in certain ways to protect endangered species.

It would take time to bargain to get people to protect environmental treasures that he cared about or accept taxation for things he felt important whether they be the traditional right-wing roads, courts and armies or other programs such as an opera house. Under either a Lindahl Equilibrium or with side payments, it should be possible to find some combination of taxes and expenditures to which everyone would agree. It just takes time and haggling, as people engage in "strategic behavior" by mispecifying their Lindahl taxes.

But even the assumptiont that we could deal with these problems, there would still be a few obstinate souls. Jeannette Pickering Ranking voted against the first declaration of the war United States entering World War II (as well as War I). (She voted present on declaring war against Italy and Germany after they declared war against the U. S.) And those countries that have home-grown terrorists could expect that they would refuse to vote for the most basic measures, even under the most severe threats.

The equivalence of majority vote and some conditions

But the familiar 50% plus one has some strong theoretical support from 1952, Dr. May said any way of deciding, a "group decision function" taking as input everybody's yea, nay or don't care, should obey the following properties. The set of inputs, which he postulated as a list of -1, 0, 1 for every voters, I will call I for shorthand
  1. It should give an answer for every possible I It should not say I don't know. I postulated some cases where I don't know might be appropriate. If two candidates for president were very close, perhaps both should win, and should they conflict on a particular decision, that decision be sent to a sortition jury or even a full plebiscite.
  2. If we swap a -1 vote from voter x with a 1 vote from voter y, it should not matter. In other words, the votes should count equally. Dr. Dahl's specified this in his definition of procedural democracy.
  3. The decision function should be unbiased. If all the 1's were replaced with 0's, and all the 0's replaced with 1's, the decision function should give the opposite result. A supermajority would favors the status quo.
  4. The decision system should be monotonic. If everyone who voted for first of the two alternatives continued to do so and then some who voted for the second switched their vote, one should not find that the function was more likely to report the second. In other words, as people switched their vote, it should make it more likely that the new alternative succeeded.
Dr. May proved that having this conditions means that the only decision is the familiary majority vote system, and of course, the majority rule fulfills these conditions.

But this only helps when there is one alternative to be decided. If there are multiple candidates, we have all the problems of voting rules and Arrow's Paradox.

One by one or multiple times

Dean Lacy and Dr. Emerson Niou have not read the combinatorial auction literature--this was Dr. Lacy's Ph.D. Dissertaion. They pointed out that when a group care about a combination of things, you cannot just have them vote one-by-one. Assume everybody in a town wants to pass two out of three bond issues. They all feel that this is what the town can afford. However, they all disagree as to which two of the three the town should construct.

In fact it is very bad. If there is one combination of bonds that everyone agrees is better than every other one, voting one by one may lead to a different result. And, voting for several issues may lead to a combination that every single voter would say was worse than some other combination! However, if each election is held separately, ... IN other words, they vote on one bond, let everyone know whether it succeeded, then vote on the next bond, etc. does help. (Kadane reported on nine states that sent several changes to their state consitution to voters. Five states that just had one proposition with all the changes had them all defeated. Four states divided the changes into individual changes and either all passed or all but one passed.)

If the votes are done sequentially, it does help a little. The combination that wins will not be a Condorcet loser that would lose to each other combinations and will not be considered the worst of the combinations by every single voter.

Dr. Lacy points out that the population could vote by set, how many want YYY? How many want YYN? How many want YNY? How many want NYN? etc. However, if there were 2000 alternatives, there would be 22000 sets. No voter, or even computer, could specify that many. Dr. Nisan discussed "languages" or ways that a bidder in an auction could give all their preferences without having to specify something for every conceivable combination of issues? Are these applicable to choices in a political system? Dr. Lacy says that a representative deomocracy can vote trade and do sophisticated voting--but a series of referendums for participatory democracy cannot. A statement he did not support.

His table six listed the results for different combinations.

  • Do the voters do better than a leader, or small group of representatives. If the voters are .50001 right and .49999 wrong, then taking a majority will be more likely right than a few leaders even if they are more expert. But, I am sure you read in history of a farsighted leader who would make peace when the population was still angry. And if everyone is probably wrong, a majority of the population will definitely be wrong. So those who say we should have wise representatives and a wise president decide things rather than the ignorant masses believe that the individuals are each more likely wrong than right. Dr. Nurmi shows this from the Condorcet voter theory or more basically, probability theory. And he shows similarly, that if people are more likely to vote their true interests than incorrectly, they are better off in a participatory democracy, than in another system. Most of the errors cancel. This is related to Dr. Surowieckis argument that people's misinformation on each side of the issue cancels, leaving the correct information in the majority determining the voting. the correct information in the majority. I mentioned that a supermajority is appropriate for the judicial rule. More precisely when some appointed group of people is in charge to make sure that every law respects individual rights, obeys the religious beliefs under which the country was founded, or is logical or budget-balanced, then when that group disagrees among itself, then the decision should go to plebiscite. Thus, a five-to-four or six-to-three supreme Court Decision on Constitutionality should go to plebiscite.

    Dr. Buchanan believes that super-majorities help favor minorities, otherwise two thirds (or less) can simply vote to tax the minority without giving them any benefits in return (July 22nd Thoughtful Thursday). On January 27th, 2010, another Nobel Prize Winner, Paul Krugman, said that unless the United States removes the requirement of 60 percent to stop fillibusters in the Senate, "we're headed for full banana-republic status." But some of the comments were negative - saying that Bush, who is the enemy in his blog, could have done anything. And Mr. Randall said the Republicans win a majority in a few years, they could undo health care reform. Nine states of U.S. require a supermajority to pass a budget under certain conditions, often if the budget is not passed in time.. California requires a supermajority for all but education and Rhode Island requires a supermajority to appropriate money for local or private purposes. But the National Conference of State Legislatures say that it is not sure what the end result of this is. I suspect that most readers are familiar with the problems California has had with its budget, some of which has been blamed on the supermajority requirement.

    Anthony McGann points out that use core/coalition/game theory/Rawlians concepts, that under majority ruling, one is most likely to be able to form a coalition to defeat some policy that one would not like. My game theory course did not cover it saw that in E. M. Barron's book.) (Dr. McGann discusses checks and balances and the writings and beliefs of Madison and John Calhoun on how these may help protect minorities. I will cover them in a future Thoughtful Thursday.) But he had some powerful diagrams of how voters or legislators might decide an issue that had two parameters. These could be a budget with the amount of spending and the amount of taxes--the difference would be the deficit or borrowing. Assume that eight voters cluster as follows at three positions (forming a triangle)

    NameNumber of Voters
    Under majority voting, there is no core, so that all could bargain for a proposal that they would like. However, if six are needed to pass a proosal, then c becomes disenfrancharged. Dr. McGann shows even more pathological cases; a status quo can remain that is nowhere near the center of the majority voters, opinions. Lani Guinier, a noted fighter for civil rights, argued that super-majorities protect minorities as well as a variety of voting rules. Yet, it was the filibuster that slowed down civil rights legislation.

    But majority rule is subject to cycles when there are three or more alternatives, A would B in a single contest, B would beat C in a single contest and but C would beat A. And Dr. Buchanan I believe from the citations I have read that Riker--he is on the list for a Thoughtful Thursday, argues that representative democracy is less likely to have cycling than a participatory democracy system and Miller (1993)was cited for the same thing.

    Obviously, the status quo is favored in super majority systems, whatever law was passed last year or last century. But as technology changes, this may not be the people, or their children, who voted for it wanted. Union rights were not important when ninety percent of us were farmers. Our fourth Amendment rights may become more important as spying technology allows a more intrusive state or more of a problem if terrorists gain the potential of genetically engineering a superbug. Or as Brunel-Petron put it, the status quo is a set of legal formalisms, not a set of outcomes. And the executives, bureaucrats and judiciary gain more power if the legislature or participatory democracy needs more votes to do something about it. An example. The Environment Protection Administration is coming out with regulations limiting carbon dioxide emissions as a pollutant. (The Supreme Court ruled that they could.) Congress persons have several proposals to block these EPA regulations, probably for two years.)

    At the end, Dr. McCann sites several articles. Voting cycles help minorities have a voice. But that better be another Thoughtful Thursday.

    for Future Thoughtful Thursdays

    1. Davis, Otto A , M. H. DeGroot and Melvin J. Hinich 1972 "Social preference orderings and Majority Rule" Econometrica 40 147 to 57
    2. Denzau Arthur T. and Robet P. Parks 1977, "A Problem with Public Sector Preferences" Journal of Economic Theory 14 454 to 457
    3. Denzau, Arthur T and Robert P. Parks 1983, "Existence of Voting-Market Equilibria" Journal of Economic Theory 30 243 to 265
    4. Diba Behzad and Allan M. Feldman, 1984, Utility Functions for Public Outputs and Majority Voting" Volume 24 1984, 1 to 2, 235 to 243, Journal of Public Economics
    5. De Donder, Philippe, Le Breton, Eugenio Peluso, "Majority Voting in Multidimensional Policy Spaces: Kramer-Shelpsle versus Stacklberg"
    6. Farquharson, Robin, 1969, Theory of Voting
    7. Kadane, Joseph, 1972, "On Division of the Question" Public Choice 13 47 to 54
    8. Kramer, Gerald H. 1972, "Sophisticated Voting Over Multidimensional Choice Spaces" Journal of Mathematical Sociology 2: 165 to 180.
    9. Koehler David H. 1975 "Vote Trading and the Voting Paradox: A Proof of Logical Equivalence" American Political Science Review 69 954 to 960.
    10. Gibbard, A. 1973 "Manipuation of Voting Schems" Econometrica 41 587 to 601
    11. Satterthwaite M. (1975) Strategy Proofness and Arrow's Conditions: Exitence and Correspondence Theorems for voting Procedures and Social Choice Functions Journal of Economic Theory 10: 187 to 217
    12. Saari D. G. (1989) A Dictionary of Voting Paradoxes, Journal of Economic Theory 48 443 to 475
    13. Saari D. G. (1994) Geometry of Voting New York
    14. Saari D. G. (2000) Mathematical Structure of Voting Paradoxes Economic Theory 15 1 to 53, 55 to 102
    15. Feld, S. L. and Grofman B. (1992) Who is afraid of the big bad cycle? Evidence from 36 elections Journal of Theoretical Politics 4 231 to 237
    16. Miller, N. R. 1980 "A new Solution Set for Tournaments and Majority Voting" American Jouranl of Political Science 24 68 to 96
    17. Miller N. 1983 "Social Choice and Pluralism" American Political Science Review 77.3 734 to 747
    18. Nakamura K. 1979 "The Vetoers in a Simple Game with Ordinal Preferences" International Journal of Game Theory 8, 55 to 61
    19. Gibbard, A. 1973, "Manipulation of Voting Schems" Econometrica 41 587 to 601.
    20. Riker, W, 1982, Liberalism versus Populism: A Confrontation Between the Theory of Democracy and the Theory of Social Chocice San Francisco: Freeman
    21. Greenberg, J. 1979, "Consistent Majority Rules and Compact Sets of Alternatives" Econometrica 47.3 627 to 63
    22. Lijphart, A. 1977, Democracy in Plural Societies Yale University Press
    23. Lijphart A. 1999 Patterns of Democracy: Government Forms and Performance in Thirty-Six Countries New Haven, Yale University
    24. McKelvey R. 1976 "Intransivities in Multidimensional Voting Models and Some Implications for Agenda Control" Journal of Economic Theory 16:472-82
    25. McKelvey R. 1979 "General Conditions for Global Intransitivities in Formal Voting Models" Econometrica 1085 to 1112
    26. Enelow J. and Hinich M. Advances in the Spatial Theory of Voting
    27. Guinier, Lani, 1994 The Tyranny of the Majority: Fundamental Fairness in Representative Democracy New York: The Free Press.
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