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Balanced Condorcet Voting


Paul Cohen
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Condorcet voting asks voters to specify on their ballots a preference for one of each (unordered) pair of candidates. The Condorcet winner is then determined if one of the candidates is preferred by more voters than is any other

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A disadvantage of this voting scheme is the potentially large number of pairs of candidates. With only two candidates, Condorcet voting is, in essence just plurality voting, because there is only one pair of candidates. But if there are ten candidates then voters must decide how to vote in each of 45 different pairs of voters; with fifteen candidates there are 105 pairs.

Ranked voting ballots are often substituted as a way to disguise this difficulty; voters may instead be asked to provide just a single list of the candidates, ordered by preference, starting with the voters' first choice. But this slight of hand does not really make matters any easier for voters. The voter must still determine a preference for one of each pair of candidates; in fact, the ordered list is in truth even more difficult to construct. Ranked voting adds difficulty by requiring that there are no loops introduced (such as preferring A to B and B to C but preferring C to A). It is in fact quite easy to derive the pairwise ranking for Condorcet voting from an available ranked list because it contains even more information.

But is that information accurate? In the case of the ranked-voting ballot the forced avoidance of loops is a special reason to question the accuracy of the ballots. A voter's real feelings about the candidates may include such loops. The voter may prefer A to B because of positions on education while that same voter may prefers B to C largely because both the voter and B are Masons. And that same voter might prefer C to A because of positions on gun control. Preferences in the real world seem too complicated to fit the excessively simple ranked model. Human psychology is sometimes not so perfectly logical.

Yet another difficulty with the ranked ballot design is that a voter may not even have a first choice; two or more candidates who seem equally qualified may share that top position. In fact, for many of the other pairs of candidates, a voter may be unable to specify a preference. Perhaps the voter truly perceives no significant difference between two candidates, but quite possibly in other instances the voter lacks a clear opinion because the voter knows so little about one of the two candidates or maybe even about both. It is far from unlikely that there are candidates on the ballot that a voter fails to even recognize. This is a difficulty that Condorcet voting shares with ranked voting systems.

So t here will probably be some candidates not included in a voter's list on a ranked voting ballot, just as there will be some pairs of candidates skipped over on a Condorcet ballot. How these missing specifications are handled when tallying the votes is critical to the election outcome, serious especially for the less widely familiar candidates.

Generally, with either ranked or Condorcet voting, the usual practice is simply to ignore the missing information on a candidate-by-candidate basis. Administratively this may be a nice easy solution but it is an approach that causes trouble for the election and especially for the less well-known candidates. In the case of ranked-choice voting (IRV), this treatment has the same effect as putting the missing candidates at the very bottom of an extended list. In effect this puts even the lowest ranked candidate on a ballot list to be counted as being preferred over the skipped candidates. For a well-known candidate, these don't-care voters may be tallied as a huge pool of Condorcet supporters.

Generally, this misinterprets the voters' intent because the voter was not in any way opposed to the missing candidate but merely did not have an opinion. The effect of this error is to seriously depress the chances for an electoral win by any but the most-familiar candidates; it enforces two-party rule by undermining the other candidates. Should the (Condorcet) pairwise, votes be derived from a ranked list, that defect infects the derived Condorcet ballot so that it also favors the most widely known candidates; the two-party system is again well protected. Deriving the pairwise Condorcet votes from an incomplete ranked list of candidates is simply a bad idea that should be dismissed out of hand unless the aim is to protect the two-party duopoly.

The fundamental flaw in both ranked voting and Condorcet voting is in failing to account for the important and probably common situation where a voter fails to indicate a preference between some pairs of candidates. Behind both of these voting systems is the improbable presumption that every voter has a clear preference between any two candidates.

Somehow forcing the voter to invent a non-existing preference, as happens with plurality voting, will lead to random vote splitting (the spoiler effect). But if not random, the alternative is that voters rely on some extraneous basis such electability, with as much of a corrupting effect on elections.

In the comments section of this article you will find a comment describing how votes might be tallied in a balanced Condorcet voting system. This is in the comments section largely because it seems only of technical interest that are likely to bore many readers. Aside from a probably small audience of voting theorists, it seems to me enough to say that there is a system that we might consider to be balanced Condorcet voting. However, I should add that while that system may be technically interesting in some quarters, I do not consider this alternative voting system a particularly viable candidate for real-world elections. Political elections should use simple methods that make voting an easy chore that is easy for voters to understood. The system described in the comments fails badly in meeting these objectives though it probably not much worse than ranked-choice voting. BAV scores well with regard to these criteria and still seems to me to be the best alternative.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)
 

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