Median Voter Theorem

10 Key excerpts on "Median Voter Theorem"

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  eBook - ePub

  Applying the Strategic Perspective

  Problems and Models, Workbook

  • Anna Getmansky, Alejandro Quiroz Flores(Authors)
  • 2013(Publication Date)
  • CQ Press

    (Publisher)

  HAPTER 3

  TOOLS FOR ANALYZING INTERNATIONAL AFFAIRS

   

  THE MEDIAN VOTER THEOREM

  The Median Voter Theorem is a powerful tool to analyze social choice. The simple argument of this theorem is that in a group of voters arrayed along some continuous policy dimension, the median voter holds the critical position that will determine the outcome of decisions. That is, the position of the median voter will be the winning position.

  Three critical conditions must hold before we can use the Median Voter Theorem to predict outcomes. Actors must have (or be assumed to have) single-peaked preferences, we must have a unidimensional issue area, and decisions must be made by a majority rule.

  Exercise 3-1. The Power of the Median Voter

  a) Why is the median voter in such a powerful position? Explain, either intuitively or using one or more numerical examples to demonstrate.         b) Under what conditions does the Median Voter Theorem apply? In which cases can we not use the Median Voter Theorem to predict the winning position?        

  Exercise 3-2. Unidimensionality

  a) Provide an example of a unidimensional policy issue related to international relations. You can use recent topics mentioned in the news, or historical examples. What makes this policy unidimensional? What would make it not unidimensional? Display the issue graphically.

      b) Using the example from part a, provide examples of three players who have different positions with regard to this issue, and locate their ideal points in the unidimensional policy space above.    

  Single-Peaked Preferences

  The Median Voter Theorem assumes single-peaked preferences in spatial models. Briefly, an actor with single-peaked preferences

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  The Economics of Voting

  Studies of self-interest, bargaining, duty and rights

  • Dan Usher(Author)
  • 2015(Publication Date)
  • Taylor & Francis

    (Publisher)

  Suppose the election is between Abe and Beth where Abe is in fact the better candidate and where each voter has a 60 per cent chance of recognizing Abe as such. Voting in this context is like choosing a ball at random from an urn containing six balls marked Abe and four balls marked Beth. An electorate with only one voter would have a 60 per cent chance of electing Abe, an electorate with three voters would raise the probability to 64.8 per cent, an electorate with five voters would raise the probability to 68.3 per cent and a very large electorate would give Abe a sure majority of the votes. It is essential for this example that voters’ judgments be uncorrelated. At the opposite extreme where voters’ judgments are perfectly correlated, Abe’s chance of winning the election remains at 60 per cent regardless of the size of the electorate. Also, in sharp contrast to other circumstances to be discussed later on in this chapter, it might be beneficial to everybody for people to abstain when they are unsure about which candidate is best and when they believe that other voters are better informed.

  The line between the Median Voter Theorem and the Condorcet jury theorem is not as clear-cut as one might at first suppose. The guardian of the ballot box sees how many people voted for each candidate, but does not see why people voted as they did. Voting is partly a game played among voters with different objectives, partly a struggle to identify policies that are best for everybody, partly a conflict among politicians seeking office for its own sake and partly an attempt to elect the most competent5 and honest leaders. The most that can be expected of the theorems is that each, in its own way, sheds some light on the process. Other voting patterns identify other difficulties that must in practice be tolerated or overcome.

  Intensity of preference

  The central proposition in economics is that, depending on initial conditions and subject to well-known qualifications, a competitive economy yields an efficient output of goods and assignment of goods to people, so that no planner, however wise, powerful or benevolent, could rearrange the economy to make everybody better off. A planner may favour some people at the expense of others, but cannot make everybody better off at once. By contrast, majority rule voting may be inefficient, recognizing only the numbers of people favouring each option in an election, but placing no weight on how deeply voters are concerned about the options they support. Sometimes this inefficiency is borne as a regrettable but necessary cost of democracy. Sometimes it is modified by the rules within which majority rule voting takes place. Sometimes it is avoided altogether by removing certain matters from the political arena. Several simple examples show what might be at stake.

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  Democracy

  • Albert Weale(Author)
  • 2007(Publication Date)
  • Red Globe Press

    (Publisher)

  In short, the voter with preferences mid-way between the most left-wing and the most right-wing voters will get his or her way. This does not mean that median voters always favour centrist policies. If the distri-bution of voters is skewed to the left or to the right, then the ideal pos-ition of the median voter may be someway to the left or to the right of the left–right ideological spectrum. However, it does mean that that median voter is in the middle of the distribution of voters, however they may be distributed along the ideological spectrum. The logic lying behind the Median Voter Theorem is reasonably straightforward. If all voters are voting and their preferences are single-peaked, then they will by definition vote for proposals that are closer to them over proposals that are further away. A voter at the mid-point of the distribution can make a proposal that coincides with his or her ideal preference and can know that this proposal will beat any pro-posal to the left or to the right. If the proposal is further to the left, then all voters right of the median position will prefer the median position. If the proposal is further to the right, then all voters left of the median position will prefer the median. Since the median position commands a majority over these other positions, it is in fact a Condorcet-winner. That is to say, it is that alternative that can beat any other alternative when pitched against it in pair-wise competition. An ideological spectrum potentially contains a large number of positions and so the winning median position will always defeat a large number of alternatives. It may seem strange that this is so, when we saw in the earlier section that cyclical (that is to say non-Condorcet-winning) majorities could be generated with just three alternatives. How does it come about that in spatial accounts of voting we can identify the Aggregation, Unanimity and Majority Rule 169

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  Conflict, Complexity and Mathematical Social Science

  • Gordon Burt, Manas Chatterji(Authors)
  • 2010(Publication Date)
  • Emerald Group Publishing Limited

    (Publisher)

  The section ‘ The distribution of ideal points: representative democracy as social choice ’ has established a number of important results for the mean ideal, and done so in a very straightforward manner. In this section, we find that the situation is much more complicated for the median Theory, Evidence and Reality 79 ideal. There is no one simple formula and an empirically based approximation may be the best we can do. The Legislative Median and Partisan Policy Wiseman and Wright (2008) [hereafter referred to as ‘WW’] look at the Democrats and Republicans in the US House of Representatives. One or other party has a majority. Each person has a policy position which can be represented as a point on a one-dimensional continuum, ‘left’ to ‘right’. In this type of situation the median person is of particular interest because the Median Voter Theorem states that the policy outcome will be the policy preferred by the median person. An interesting question is therefore how the overall median, m , in the US House is related to the Democrat median m (D) and the Republican median m (R) ( Fig. 5.1 ). In their abstract the authors say: We show that the median legislator in the US House is unambiguously closer to the majority party median than to the minority party median. An important implication of this finding is that the median legislator is predisposed to support the majority party’s policy agenda. Thus, in the event that the majority party organization exerts no influence over the legislative process, and in the event that all policies then default to the legislative median, policy outcomes will still substantially favour the majority party over the minority. We demonstrate that the legislative median moves predictably toward the majority party in response to changes in majority control and the size and ideological homogeneity of the two parties. Consequently, the median legislators’ partisan predisposition increases and decreases in response to electoral change.

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  Application of Fuzzy Logic to Social Choice Theory

  • John N. Mordeson, Davender S. Malik, Terry D. Clark(Authors)
  • 2015(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  Hence as the number of these coalitions increases past three, a fuzzy core will exist in two-dimensional spatial models. To the extent that the number of players potentially increases the number of winning coalitions, an increase in their numbers will result in a greater likelihood of a core. We conclude the chapter with a short history of the Median Voter Theorem. Majoritarian voting is an ancient method of group decision making. There is no clear statement of the Median Voter Theorem until around 1950. Aristotle’s analysis of political decision making written in 330 B.C. made no mention of a pivotal or decisive voter. Condorcet (1785) discovered the idea of a pivotal voter and noted how the accuracy of decisions can be improved by majority decisions, but made no clear statement of the Median Voter Theorem. The Median Voter Theorem was first stated by Black (1948) and extended by Downs [9] to representative democracy (1957). 202 6. Single Peaked Fuzzy Preferences: Black’s Median Voter Theorem 6.5 Exercises 1. [14] Let ρ be an FWPR. Then π , the strict preference relation strict preference relation with respect to ρ , is said to be partial if, for all x, y ∈ X, π ( x, y ) > 0 ⇐⇒ ρ ( y, x ) = 0 . An FWPR ρ on X is regularly acyclic if for all { x 1 , x 2 , x 3 , . . . , x n -1 , x n } ∈ X, π ( x 1 , x 2 ) ∧ π ( x 2 , x 3 ) ∧ . . . ∧ π ( x n -1 , x n ) > 0 implies π ( x n , x 1 ) = 0. Let ρ be an FWPR. If π is regular, then prove that the following properties hold: (1) ρ is max-min transitive implies ρ is partially quasi-transitive. (2) ρ is weakly transitive implies ρ is partially quasi-transitive. (3) ρ is partially quasi-transitive implies ρ is regularly acyclic. 2. [14] Let L⊆ F ( N ). Let ρ ∈ FR n and set ˜ P ( ρ ) = { ( x, y ) ∈ X × X | ∃ λ ∈ L , π ( x, y ) > 0 , ∀ i ∈ Supp ( λ ) } .

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  Game Theory in the Social Sciences

  A Reader-friendly Guide

  • Luca Lambertini(Author)
  • 2011(Publication Date)
  • Routledge

    (Publisher)

  R = 1/2, all voters are in fact totally indifferent as to which party to patronize precisely because Left and Right have become identical in all respects. This entails two related consequences:

  • if xL = xR = 1/2, the median voter is not necessarily pivotal, while (or, because)

  • any voter is potentially pivotal. Shall we take the result of the Median Voter Theorem for granted, i.e., shall we buy it at its face value, or is there more to it? This delicate issue is the subject of the next section.

  6.3  The robustness of the Median Voter Theorem

  As I have mentioned above, the linear segment may represent the set of all admissible policy stances a party or candidate may take, concerning the pension system, income taxation, etc. If this is the interpretation of the Hotelling–Downs model, then the first possible extension consists in allowing for more dimensions to jointly define a candidate's political platform. It can be shown that the basic result is robust to such a generalization (see Davis et al., 1972; Hinich et al., 1972, 1973; Slutsky, 1975; Austen-Smith, 1983; Calvert, 1985; Ansolabehere and Snyder, 2000), although in this case a pure-strategy equilibrium may not exist – the mixed-strategy equilibrium has been investigated by McKelvey and Ordeshook (1976) and Kramer (1978).

  If voters (or their preferences) are not uniformly (or even symmetrically) distributed along the segment, then there is no guarantee that the Median Voter Theorem may hold. The last 50 years of Italian politics constitute an evident illustration of the consequences of polarizing political preferences: while during the so-called First Republic

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  The Homevoter Hypothesis

  How Home Values Influence Local Government Taxation, School Finance, and Land-Use Policies

  • William A. Fischel(Author)
  • 2009(Publication Date)
  • Harvard University Press

    (Publisher)

  With only a small stake in any given firm, business stock-holders have little incentive to pay attention to their internal gover-nance. Now it is time to defend my emphasis on the role of homeown-ers in municipal affairs. The median-voter model of politics, which is the social-science name for majority rule, was first elaborated by Howard Bowen (1943). His hypothesis was that under majority rule, the householder who had the median income, or, I would add, median home value, in the com-munity would get the public services and taxes he demanded. This would be true by definition if all residents simply voted on all issues that had an economic effect. But the median-voter model goes further and asserts that this result will hold even in representative govern-ments. Elected officials select budgets and taxes “as if” they had been voted on in a plebiscite. (To be precise, the model should be called the The Median Voter in Local Government Politics 87 “median-income-voter” or the “median-home-value voter” model, but I will continue to use the economists’ shorthand and omit the precise economic characteristic along which voters are lined up.) The median-voter model has been subjected to an extensive set of statistical tests in the economics literature, and most of these tests have involved samples of local governments. The consensus as I read it is that the median-voter model holds up quite well in comparison with its alternatives. The alternatives are (1) that bureaucrats expand the level of public services to increase their own wealth and power (William Niskanen 1971), (2) that concentrated economic interests lobby suc-cessfully for a set of goods of little interest to the median voter (George Stigler 1971), or (3) that some combination of bureaucrats and special interests set all-or-nothing voting agendas so that the median voter has to select more than she wants (Romer and Rosenthal 1979).

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  Public Finance and Public Policy

  A Political Economy Perspective on the Responsibilities and Limitations of Government

  • Arye L. Hillman(Author)
  • 2019(Publication Date)
  • Cambridge University Press

    (Publisher)

  We have been assuming that the preferences of voters have the property of being “ single peaked ” . Single-peaked preferences are de fi ned in Section 11.9, where we shall see that single-peaked preferences of voters ensure a stable median-voter equilibrium. 10 To see why this is so, we consider a population with n voters. Average MB of the population is: MB A ≡ P n j ¼ 1 MB j n : With equal sharing of costs and P = MC for the public good, the preferred supply of the voter in the population with the average valuation of the public good is determined by: MB A ¼ c n ¼ MC n and therefore: n MB A ¼ X MB ¼ MC : A median voter who happens to have the average MB of the population therefore chooses ef fi cient public spending. 11.5 The Median Voter and Public Spending 351 People with higher incomes may want more of a public good than people with lower incomes (that is, the public good is a normal good). Then, as shown in Figure 11.5b , the average valuation of the public good in the population exceeds the median valuation. In the majority-voting equilibrium, with the median voter decisive, less-than-ef fi cient public spending is chosen. 11 Voters with high incomes could have low valuations of public goods. Low-income voters may want publicly fi nanced shared recreational amenities, good government schools, and personal security from the police. High-income voters might use a private swimming pool, be a member of a private country club, send their children to a private school, and have private security guards. The valuation of public goods of the median voter then exceeds the average valuation, and majority voting (or choice by the median voter) results in over-supply of a public good relative to ef fi cient supply. Depending on whether low-or high-income voters value public goods more, the outcome of majority voting with equal taxes can be under-supply or over-supply of public goods.

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  Elections as Instruments of Democracy

  • Frank B. Golley(Author)
  • 2000(Publication Date)
  • Yale University Press

    (Publisher)

  There is, however, much controversy about the correspondence be-tween Downs's theory and the empirical facts of party competition. 3 Because only the winning party needs to be near the citizen median to create congruence, the majoritarian vision need not depend on Downs's strategic parties. It can encompass other two-party models in which incumbents face challengers who over time offer a large array of possible alternatives. 4 The parties may not be anticipating voter preferences or even be able to estimate them, at least initially. With the voters always choosing the more preferred alternative, eventually the election winners will be at or near the median voter. This is what traditional mandate versions of majoritarian theory seemed to expect, as discussed in chapter 4. We can even imagine a version of this in which true party positions are not revealed to the voters until the party has held office. So voters begin by randomly choosing a government, keeping it if it turns out to be close to their preferences, discarding it if it does not. Again, eventually the voters find and hold on to governments close to the median. In these less strategic versions, if the system were starting from scratch as a democracy, it might take some time for random offerings of party policies, especially if only retrospectively discovered by voters, to converge on the median. As all the democracies in this study except Spain and Greece had been operating as democracies for some time even at the earliest points here consid-ered, we would expect from these theories, too, to find at least one party near the median, unless there were radical changes in the position of the electorate. Given the continuity we see over time in the location of the citizen median and the parties, as well as what we know about public opinion configurations, such major changes seem to be rare.

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  Referendums and Democratic Government

  Normative Theory and the Analysis of Institutions

  • Maija Setälä(Author)
  • 2016(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  Each voter has an ideal point, and he or she votes for the candidate or the party which represents the position which is the nearest to their ideal point, the distance measured in Euclidean terms. The idea of equilibrium conditions is based on ‘the symmetry of dis- agreement’, in which the opposing preference orderings ‘balance out’ each other (Plott 1967). If the number of voters is odd and if the prefer- ence ordering can be paired in such a way that the orderings in each pair are opposite to each other, then the majority preference ordering is transi- tive. The situation can also be described as a tie which is broken by the remaining unpaired ordering, the majority preference ordering being identical to this ordering (Miller 1983, 739). For example, in figure 2.1b voters’ a and c preference orderings are the opposite and balance out each other and the alternative x preferred most by the remaining voter b is the majority winner. Plott has demonstrated a sufficient condition for the existence of a major- ity winner in a multi-dimensional space issue. McKelvey (1976), among others, has discussed the general conditions for the existence of a major- ity winner – that is, ‘the median to all directions’ – in multi-dimensional voting situations. It has been concluded that a majority winner rarely exists in these situations. Moreover, McKelvey has proved in his ‘chaos theorem’ that if there is no median to all directions, the transitivity of majority rule fails entirely and a majority preference cycle covers the whole alternative space. There are some other ways out of the chaos created by cyclical majori- ties. All decisive decision-making institutions impose equilibria upon the majority cycles. The outcomes generated by institutions may be called Referendums and Democratic Government 26

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