Chapter 7 of Analyzing Politics  

K.A. Shepsle

A Summary 

Voting Methods

  • Which voting method is chosen will affect the outcome given heterogeneous preference ordering.
  • Examples of types of voting system:
    • Simple plurality: Each voter casts a vote for a single alternative and the alternative with most votes wins.
    • Plurality runoff – single vote, single alternative, and two alternatives with most votes move to next round in which balloting is repeated.
    • Sequential runoff: single vote, single alternative, then alternative with fewest votes eliminated and process repeated until there is one alternative left.
    • Condorcet Procedure – pairwise round robin tournament.
    • There are many more.
    • Given static preference ordering over a set of alternatives each method is capable of producing a totally different outcome. Thus the rules for preference aggregation matter a lot.
    • May need to think about the costs to voters in terms of how demanding a system is, and how much information they will need to gather in order to vote.
    • Also, the system chosen may not only change outcomes, but change the alternatives, as which candidates, policies are proposed will depend upon their ability to triumph. Candidates are endogenous to the voting system.
    • How then do we talk about the will of the group when using different methods reveals different group preference results?

 Electoral Systems

  • The voting method in elections will depend upon whether the core value of the system in question is governance or representation. The former is associated with plurality means of voting – political representatives are able to act decisively and govern. The latter is associated with proportional representation whereby those elected represent the beliefs and preferences of the electorate. Generally plurality voting is for candidates, and PR voting is for parties.

 Plurality: First past the Post

  • Each voter gets one vote and the candidate with most votes (not necessarily a majority) wins. If the constituency only gets one member they will not be very representative of the electorate assuming they are diverse bunch. If district magnitude is larger than the system will be more representative of the heterogeneity of the electorate, but it also means a bigger legislature and this can be harder to govern and ultimate take action on public policy which is surely the job of government.
  • There are different types of plurality voting:
    • Single non-transferable vote: one vote, but the k highest vote getters are elected, when k is set beforehand.
    • Limited vote: more than one vote, but still allowing for k winners
    • Cumulative vote: voters may cumulate their votes for candidates e.g. cast both for 1st preference. This encourages minority representation as well-organized minority candidates can win seats.
    • The equilibrium tendency of plurality systems depends upon the number of possible candidates in a district. Forces will either be centripetal (candidates converge to median), or centrifugal (candidates distribute along the spectrum).
    • Cox shows that when cumulation is not allowed, if the number of candidates is small enough relative to the number of votes that can be cast per voter then centripetal forces will dominate. But if the number of candidates is large then centrifugal forces operate to disperse the candidates along the continuum in equilibrium. When cumulation is allowed, the centrifugal forces always operate. E.g. Japan where there are 3-5 candidates per district, but only one vote allowed, there is no observed clustering on the median voter.

 Plurality: Single Transferable Vote

  • Each voter reports his entire preference ordering. One a candidate reaches a quota of voters he gains a seat and the second preferences indicated on his ballot papers are distributed to the relevant other candidates. In this way another candidate may reach the quota and the process is repeated until the number of candidates to be admitted is reached. If upon transfer no other candidate has enough votes to make the quota, the candidate with the least first place votes is eliminated and his second preferences are distributed.
  • This system means that a candidate has to energize his own supporters and to get listed high up the preferences of those supporting other candidates to get their reassigned votes.

 Proportional Representation

  • The aim is produce a legislature that mirrors the preferences of the whole society. A PR system tends to reproduce the main social cleavages.
  • Systems differ primarily in how they deal with fractional seats (a candidate get 4.35% of vote but can’t have 4.45 seats), and what the specified minimum is in order to get at least one seat (in Poland this is 1/450th of the vote, in Germany it is 5% – high thresholds make the system more disproportional).
  • Duverger’s Law suggests that FPTP with single member districts are strongly associated with two party/candidate competition. Third parties will not enter as they rarely have a chance of winning as voters will not waste votes on candidates that cannot win, even if they best represent their preferences. This is supported empirically. The second part of the law states that PR systems are associated with multiparty systems. Whilst this is supported empirically the analytical link is not well understood.


  • FPTP systems resolve conflicts before the legislative process begins. This allows the winning party, who will often command a majority, to govern in the manner in which they see fit, constrained by their campaign promises and the need to win the following election etc.
  • PR systems defer this conflict until the legislative process begins. They reflect rather than resolve political conflict, and the legislative process is a means of discovering the manner of resolution.

One Comment

  1. Posted June 13, 2011 at 3:11 pm | Permalink | Reply

    ‘Generally plurality voting is for candidates, and PR voting is for parties’
    DPR Voting makes this distinction and combines both methods in one electoral system.
    Single member constituencies, a plurality election, makes election of local constituency MPs simple, and a party vote, because the system should not give more voting power to any one party than the people are prepared to do with their votes.
    Google DPR Voting

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