APPENDIX 5
CRITERIA FOR JUDGING VOTING SYSTEMS
THE BORDA COUNT AND APPROVAL VOTING RECONSIDERED
After Anthony Gottlieb's July 26, 2010 very good article on voting systems appeared in The New Yorker, I had a brief exchange with him. In that exchange, Gottlieb made a reference to Sir Michael Dummett's "Principles of Electoral Reform" (Oxford University Press,
1997) which peaked my curiosity. As a result I bought and now have read twice what I found to be a very important book on voting reform which, although focused on the issue in the British context, is surely a must read for any British or American citizen interested in this vital issue.
The underlying focus of Dummett's book is on the issue of what criteria are the only reasonable ones for picking the most representative single candidate for offices like representative, senator and president on the basis of voters' preferences. Dummett's answer to this question, especially his exposition on the Borda count, has compelled me to rethink some issues on how to assess alternative voting systems.
The purpose of this note is to set out how I now see some of the issues here in light of my reading of Dummett.
Prior to reading Dummett, I considered the Condorcet criterion to be the most sensible one in judging the desirability of alternative voting systems. The Condorcet answer to who is the most representative candidate in single-winner, multi-candidate elections is the candidate who can beat all the other in all the pair-wise
(one-to-one) contests possible from the field of candidates. According to this criterion, the greater the tendency of a voting system to choose the Condorcet candidate where one exists, the better the voting system is.
If every voter can rank all candidates individually one by one, it is possible using computers to determine the Condorcet winner from such rankings. The problem that arises here is that although such individual rankings are transitive (i.e., if A is preferred to B which is preferred to C, C cannot be preferred to A) aggregate ones may not be leading to the Condorcet paradox.
In such situation where in a four man election, for example, voters favor A over B, B over C, C over D and D over A, a Condorcet winner cannot be identified. Given that it is easy to demonstrate such possibilities in aggregating individual preferences into election results, the Condorcet criterion ceases to be a valid basis for judging the effectiveness of alternative voting systems in such situations. In such a situation, I have argued that the criterion underlying approval voting represents a second best solution to the issue of evaluating alternative voting systems. But after reading Dummett, I probably would revise this; of which more later.
Until I read Dummett, I had always thought of the Borda count as an alternative voting system, not as an alternative criterion per se for determining which candidate is most representative given voters'
individual preferences. Dummett points out an interesting characteristic of what I would call the standard Borda count that suggests otherwise.
This can at first best be seen by looking at a hypothetical Borda election in which we consider the preferences of a single voter who alone votes in an election with a field of ten candidates. In a standard Borda election of n candidates, a candidate listed first by a voter gets n-1 points, a candidate listed second gets n-2 points and so on until the last candidate listed who gets n-n or zero points. Thus in such a ten man election the candidate ranked first gets under the Borda count nine points.
It is easy to see, given the eight points of the second ranked candidate, that these scores represent the number of votes each candidate would receive given the voter's preferences in all of the pair-wise (one-to-one) contests possible from the field of candidates.
Since this would be true for each of the voters in a standard Borda election, it follows that the score each candidate gets represents the total votes each would receive in all the pair-wise contests possible from the field of candidates.
This is of such significant importance that it is well worth quoting in detail from Dummett's exposition on this matter which is as
follows:
The method proposed by Borda...may again be explained in terms of
comparisons by pairs. Given the preferences of the voters, we again
imagine that each candidate is pitted against each of the others
taken in turn. This time, however, we take account, not just of
which out of a pair of candidates beats the other in a contest
between them, but of the number of votes that would be cast for each
if all voted sincerely. For each candidate, we add together all the
votes cast for him in all his contests with other candidates,
regardless of which of them he won and which he lost. The grand
total is his BORDA COUNT. This suggests a rival criterion for which
candidate should be considered the most representative. Ignoring
majority preferences, we might hold the most representative
candidate the one who has the highest Borda count. (Sir Michael
Dummett, Principles of Electoral Reform, Oxford University Press,
2004 reprint, p. 62).
It is clear from reading Dummett that he views the Condorcet and Borda criteria as the most plausible ones in determining who is the most representative candidate in single constituency elections (i.e.. for US representative, senator and president). After reading Dummett both criteria seem equally plausible to me. As Dummett points out there can be no proof of which is the sounder of the two.
Nevertheless, for those not imbued with what Dummett labels as "the mystique of the majority" or Professor Robert Z. Norman calls the "sacredness of the majority," perhaps a stronger case can be made for the Borda approach assuming that sincerity is widely extant in the voting process. As Dummett put the issue here:
It seems clear that Borda's criterion is the soundest method of
identifying the candidate who is most generally popular with the
electorate, or at least the most acceptable." (p. 71)
As Dummett points out numerous times, in multi-candidate elections there is no voting system that will not sometime offer an advantage to tactical voting. While the Borda system is no exception to this, it does have two characteristics in the area of tactical voting which may make it something of a unique voting system.
On the one hand as Dummett points out:
But even a majority of voters [under this system] has no way of
voting that will ensure that a given candidate will obtain the
highest Borda count, however the remaining voters decide to fill in
their ballot-paper. No majority can IMPOSE its will [as it can under
other voting systems]. (p. 86)
On the other hand:
The Borda system offers a fair incentive to tactical voting (p.86).
On this score Dummett rightly points out that:
The system is vulnerable to tactical voting in the sense that if a
great many voters indulge in it, the outcome is likely to bear
hardly any relations to their true preferences." (p.86)
The most common example of such tactical voting is the situation in which voters rank the candidate who most threatens their first choice last although otherwise they rank that candidate highly. The anecdotal evidence from many situations where the Borda system has been used in places like university departments to make hiring decisions and the like, is that it all too frequently had led to surprising and unrepresentative results. Given this it is not surprising that, with the exception of a Donald Saari, many academics do not seem to be so enthusiastic about Borda elections.
While it is not so clear to me the extent that this would be a problem in public elections, Dummett suggests in the conclusion to his book
that:
the Borda system is arguably too vulnerable to tactical voting to be
adopted [for single-member constituencies]. (p. 184)
Should this not be the case in public elections, the Borda system could surely be a desirable system for those who want to have a system of ranking for voters as opposed to a ranking system like instant runoff (IRV), or preferential, voting which Dummett's book makes clear is a very poor voting system indeed.
In general voting theorists like Dummett consider that voting systems that minimize tactical voting are preferable to those that do not. While there is merit to this position as illustrated by the tactical problems that can arise under the Borda system, I have some reservations on how this issue is generally treated in the technical literature on voting.
In discussing tactical, or strategic, voting, most commentators, Dummett included, do not distinguish between various types of tactical, or strategic, voting and their desirability or undesirability in terms of identifying the most representative candidate.
In looking at the issue of tactical voting, I would submit that we can identify three basic types: 1) Tactical voting that clarifies, 2) Tactical voting that misrepresents, and 3) Tactical voting that manipulates. In the first case, it is not so clear to me that tactical voting would ipso facto be undesirable in terms of identifying the most representative candidate for single-member constituencies.
Despite a Donald Saari, it would be my contention that a distinct advantage of approval voting is that it encourages voters to vote both sincerely and strategically at the same time. Such voting allows voters to better reflect their preferences given the constraints of other voters' preferences. The 2000 Florida presidential election is a case in point. It is true that had the election been run under IRV that Gore would certainly have won because he would have been the second choice of most Nader supporters. But the same thing would surely have been likely under a system like approval voting in which voters can give a vote each to the candidate or candidates they support with the candidate having the most votes winning.
As far as I can see deliberate misrepresentation of preference is not an advantageous strategy under approval voting. This does not mean that assumptions about the constraints voters face with respect to assessing others' preferences will always be correct. But the information needed to assess this is likely to be more accessible and easier to understand than for other systems that rely upon rankings in the voting process. This I view as a distinct advantage of approval voting over other systems like Borda, Condorcet and IRV.
In addition, tactical voting that manipulates the expression of other voters' preferences in the voting process hardly seems a possibility under approval voting. This surely is not the case with a system like IRV where parties can use "How to Vote Cards: to manipulate the outcome as parties are purported to have done in Australia.
In summary, while like any other systems in multi-candidate elections approval voting is not immune to tactical voting, strategic voting under that system is likely to be more benign in that such voting allows voters to better reveal their preferences given the constraints they encounter without serious misrepresentation or manipulation.
In his book Dummett focuses on the criteria of Condorcet and Borda because he did not know, and was unable to think of, any other that approaches either in plausibility. One of the challenges Dummett made in his book was for the reader to come up with an alternative criteria for determining who is the most representative candidate from the field of candidates in an election.
After reading Dummett and reflecting on this, I would think that the ability of a voting system to find the candidate acceptable to the largest fraction of the electorate is an equally plausible criterion. On this score, approval voting must certainly rank quit high as a desirable voting system for elections in single-member constituencies such as for US representative, senator and president. Since the Canadian scholar Ka-Ping Yee in his simulations of voting systems found considerable similarities in the results of the Condorcet system and approval voting, it may also rank quite high in terms of the Condorcet criteria as well.
Given this and given the largely benign aspect of strategic voting under approval voting suggested above, people may find it attractive as Dummett suggested in his list of further reading at the end of his most interesting book. It may well be the best alternative voting system currently available to us.