CHAPTER 9
PEOPLE THINK VOTING SYSTEMS ARE SIMPLE,
BUT IT TURNS OUT THEY ARE NOT
During the time while I was putting this book together, I received an e-mail from Clay Shentrup to which I responded by sharing with him the text of my review of Poundstone's book on Gaming the Vote. As a result, Clay very kindly posted a copy of the text on the range voting website. In response to that posting, I received a very thoughtful critique of my support for approval voting which led to an exchange two parts of which I include as a chapter in this book.
The following should give the reader a feel for some of the complexities involved in thinking about voting systems as well as to help clarify some of my thinking on issues here. The incident and the exchange also highlight the very useful public service that proponents of range voting have rendered for which I am very grateful.
An Initial Exchange
February 9, 2009
Bruce Gilson, Thank you for the following to which I respond below with a copy to Clay Shentrup amongst others.
John Howard Wilhelm
Date: Thu, 29 Jan 2009 18:23:32 -0500
Subject: Your advocacy of approval voting
From: "Bruce R. Gilson"
A correspondence between you and Clay Shentrup, posted on the Range Voting group, relating to William Poundstone's "Gaming the Vote," prompted me to write this note.
You apparently believe that the ideal election reform would be the institution of approval voting, as advocated by Brams and Fishburn. My own belief is that approval voting has one serious flaw, which makes it beyond consideration.
In approval voting, you can choose to approve a candidate or not approve, but there is no distinction between "not approving" and "disapproving." If I am voting in an approval-vote election in which there are, say, three candidates, and my chief intent is to prevent the election of one who is, in my belief, a disaster, I must vote for both of the others, EVEN if one is a candidate about which I know nothing at all. Specifically, if the candidates are Abe Lincoln, Joe Smith, and Adolf Hitler, I must vote for Smith as well as Lincoln. This is a terrible way to run an election.
You dislike range voting because of some mumbo-jumbo about comparing utilities. But at least it allows me to cast a vote FOR someone as well as one AGAINST, which approval voting does not.
When I first read Brams' book, it immediately prompted me to come up with the idea of "approval-disapproval" voting -- where a voter has THREE choices regarding a candidate: to approve, disapprove, or be neutral. This is, in fact, a very simple version of range voting. It is not much harder to implement than approval voting, and remedies approval's flaw. I cannot understand the attitude of approval voting supporters in this regard; the very first time I was exposed to the idea of approval voting, I rejected it out of hand, and why people continue to advocate it mystifies me.
--
Bruce R. Gilson
Bruce Gilson, It was kind and generous of you to take the time to respond to my correspondence with Clay Shentrup and I wish to thank you for it. While I have basic disagreements with the supporters of range voting, the exchanges I have had with them have been extremely useful for me in terms of getting a better understanding of some of the issues concerning voting systems and reform. In this sense, I would like to use this opportunity to clarify a number of points:
Why I support Approval Voting, my difficulties with the voting system that you advocate, which I first came across in reading Professor Claude Hillinger's article "Utilitarian Voting," and why my concerns about comparing utilities involves something much more substantive than mumbo-jumbo.
In explaining my advocacy of approval voting, I would like to start with a statement I made in the first chapter to the book I have put together on Third Parties and Voting Reform: The American Dilemma. It is as
follows:
A voting system is a mechanism for combining the wishes of
individuals into a decision for society or a group of people.
In judging a voting system's performance two questions need to be
asked:
1) How well does the outcome represent voters' desires?
2) How conducive is the system to giving the voters a
reasonably wide, as opposed to a narrow, range of
choices?
On both of these scores, I would argue that approval voting does quite a good job and would cite as evidence of this how the system would have operated had it been in place in the 2000 Florida presidential election.
It would be my contention, that under approval voting those who voted for Ralph Nader would have been able to also vote strategically and in most cases would have also cast a vote for Al Gore. Given this, the results of the Florida election would have much better reflected the real choices amongst those voters whose votes were counted. It is clearly the greater range of choices in casting votes under approval voting that promotes this.
My employer, The American Mathematical Society, uses approval voting in the election of its officers as do a number of other professional societies as you may well know. From talking with Dr. John Ewing, who just retired from being the executive director of the Society, I have the impression that the members of the society have been satisfied with the system and its results. It is not my position that approval voting is an ideal system, which I doubt exists, but is the best system realistically available to us currently. It has the distinct advantage of getting rid of the wasted vote syndrome and also the spoiler role and as such is surely a system conducive to opening up our political processes to third parties--something which I believe the country sorely needs.
Your and Professor Hillinger's proposed system of voting is an interesting variant on approval voting. But in looking at voting systems one has to take an important consideration into account. And that is, that a voting system has two parts: 1) A mechanism of casting votes (one vote, multiple votes, ranking, scoring) and 2) An algorithm to turn the pattern of votes cast into results. In looking at voting systems the focus is frequently on the former at the expense of the latter--a flaw which I feel infests the the views of many of the advocates of instant runoff voting. In the case of the system you advocate, my reservations focus on the second part--the algorithm used to turn the voting pattern into results.
Although I have not seen an explanation of how the algorithm works in the case of your system, I would presume that it would entail counting the positive votes for each candidate and then subtracting the negative votes for each candidate with the winner being the one with the highest number of remaining votes. From my perspective, I believe that such a system has some clear distinct disadvantages.
First, it may not give each voter an equal impact on the outcome. Let me illustrate by a simple example. Let us say that we have 200 voters in an election between two candidates with 99 voting for one candidate and 99 voting for the other. If the 199th and 200th voters are a husband and wife who vote for opposite candidates, the voting remains at a tie. Frequently in such a situation, people say that one vote cancels out the other. This is a misnomer, in reality they neutralize each other. But let us say in this situation that we allow your negative vote and the husband exercises it and does cancel his wife's vote out. That gives his candidate a one vote lead, the same result you would have if the wife were not permitted to vote and the husband was. I find such a situation a "terrible way to run an election."
In the case of an approval voting election the problem here ought to be quite apparent. Let us say you have an election consisting of three candidates, A, B, and C. And let us say that 50% of the voters find both A and B equally acceptable, 10% approve of only B and the remaining 40% only approve of C and every voter votes sincerely. In this case under approval voting, B would be the winner with a 60% approval rate. Now let's assume that half of C supporters detest B for ethnic, religious or ideological reasons and vote accordingly under your system. In this case A would emerge as the winner with 50% of the consolidated votes and B, who surely is the Condorcet candidate would lose. I do not find such an outcome encouraging either.
Second, such a system undermines one of the strong points that along with Brams and Fishburn I believe approval voting has. And that is its tendency to discourage negative campaigning. If you allow negative voting as under your system, I do not see how you can but go in the opposite direction with an even stronger incentive than under our current system towards negative campaigning.
In making my point here, I focused on the usual criteria used to judge how well a voting systems reflects voters' wishes, its propensity to elect the Condorcet candidate. As Professor Hillinger's piece on utilitarian voting emphasized, range voting uses a very different criterion in judging voting outcomes--how well they result in overall voting satisfaction in a utilitarian sense of the greatest satisfaction for the greatest number. On this score, talking about the validity of interpersonal comparisons of utility is not mumbo-jumbo.
As Professor Hillinger acknowledges, mainline, or as he puts it "orthodox," economics considers interpersonal comparisons of utility to be impossible. Hillinger attributes this to conservative ideology.
But as my example of Abba Lerner illustrates in the piece you read, this certainly is not a valid position; if anything, most knowledgeable economists would place Lerner on the left end of the professional spectrum.
The point about the impossibility of interpersonal utility comparisons is not a minor point in economics as a discipline. It underlies much of the thinking about welfare economics in the profession and its conclusions profoundly influence the tools that we use to examine issues in area like industrial organization, trade theory and things like cost benefit analysis. It is interesting that in Clay Shentrup's recent communication with me he actually put the issue very well when he said, "If you do not acknowledge interpersonal comparison of utility, then the only thing you can look at is ordinal preference and Pareto efficiency." Precisely!
But I would put the issue somewhat differently: If you cannot make interpersonal comparisons of utility, then the only thing you can look at is ordinal preference and Pareto efficiency. In looking at utility and satisfaction in judging an economic situation or an election the real issue is that of the intensity of interpersonal utility. And that we cannot determine for the reasons given by Abba Lerner in the quote I took from the third chapter of his classical book on The Economics of Control. Neither Clay Shentrup, nor the others have given any cogent reasons why Lerner's logic is wrong. Until they can I do not see how one can but conclude that they are using an invalid criterion for determining how effective different voting systems are. If your assumptions are invalid, conclusions based on them certainly cannot be considered valid.
In the case of the proponents of range voting I think that this is something of a tragedy. The recent piece that was sent to me authored by Michel Balinski and Rida Laraki on Election by Majority Judgement is an example of a voting system with some of the flavor of range voting, but surely based on a much firmer foundation in terms of logic. Yet in reading that piece, my general impression is that in assessing their results they were operating more from the perspective of the ordinal approach in judging their proposed voting system, not from a questionable cardinal approach based upon an invalid assumption of interpersonal utility comparisons. Proponents of similar voting systems might benefit by following their example and not that of the proponents of range voting.
Further Clarification
March 4, 2009
Bruce Gilson, Once again, thank you VERY much for the following thoughtful observations to which I want to respond below. But before I do, I do want to thank you for being such a really wonderful interlocutor.
Date: Tue, 24 Feb 2009 14:53:38 -0500
Subject: Re: Another Follow-up Response from J. Wilhelm
From: "Bruce R. Gilson"
To: John Wilhelm
Your very long letter seems to reflect a lot of thought. But it still fails to counter the point that for me is the most serious defect of approval voting, the fact that in a muticandidate election, there are usually three classes of candidate for a typical voter:
1. Those that the voter likes well enough that he would be happy to see
win,
2. Those he dislikes enough to want to do all he can to defeat, and
3. Those about whom he is indifferent, either through lack of information
or simply because their issues are not his issues.
In approval voting, the voter is forced to treat the third class of candidates as if they were one of the other two, and cannot truly vote sincerely. A real-life situation for me would have been the 2008 Republican primaries, had there been approval voting. There was in particular one candidate, Mike Huckabee, whom I disliked intensely, because on almost all issues he and I were opposed; if he had been the nominee I would probably have voted third-party or abstained in November. My preferred candidate, Rudy Giuliani, was already out of it by the time I go to vote, but my second choice, John McCain, was still very much alive (and of course was the ultimate nominee). So in plurality voting my choice was clear: McCain. But had there been approval voting,I would have had to contend with Mitt Romney.
If my first priority was defeating Huckabee, I would have had to give a vote to Romney as well as McCain (and Giuliani; it certainly would not have hurt to give him a vote too in an approval election!); if in the end it came down to a Romney/McCain contest, I would thus have in effect disenfranchised myself. On the other hand, if my first priority was nominating McCain now that I knew it would not be Giuliani, my choice in approval would have been to vote for Giuliani and McCain, but NOT for Romney. If in the end it turned out to be a Romney/Huckabee contest, my vote would have been just as wasted as it would have been in Plurality.
My contention is that this situation is not rare, and in fact would be even more frequent if elections were held under approval because there probably would be more candidates running, since there was more likelihood of a dark horse winning.
And I do not think that you have really seriously considered this problem.
Bruce R. Gilson,
In responding to your reservations about approval voting, I would like to start with a theme that Sir Michael Dummett touched upon in his interview in the October 2006 issue of Social Choice and Welfare (Vol. 27, No. 2). In the interview, Sir Michael made the point that it is not "possible to have a voting system that always denies advantage to strategic voting." That is, as I believe it is now well established in the technical voting literature, it simply is not possible to come up with a voting system that makes it impossible for anyone (a voter) to gain any advantage by strategic voting.
If one looks at the technical voting literature, a distinction is often made between sincere voting and strategic voting. From an analytical perspective, this certainly makes sense if one is trying to analyze how well various voting systems work in terms of reflecting voters' desires in an election outcome. But in reality, as I have argued elsewhere, there is a false dichotomy here in terms of voters representing their preferences in casting their votes. A sensible vote for voters who want to have the most impact in casting their votes in an election is surely one that takes both into consideration, their sincere desires and a realistic assessment of the impact of the various votes they could cast.
In the case of plurality voting, voters are ofter faced with a cruel choice in a system in which they can only cast one vote. And that is should they, like Nader voters in Florida, vote their conscience and waste their vote, or vote strategically and have a concrete impact upon the real choice they face, a choice between a Bush or a Gore? An advantage of approval voting as I see it is that given that voters can cast a vote each for any of the candidates they favor, they always have an incentive to give a vote to the one candidate whom they most favor. Doing so under approval voting does not deny them the possibility of voting strategically as well, for example Nader voters voting for Gore as well because of an assessment that Nader is not going to win in any case.
Now in voting for their favorite candidate, voters have to ask themselves an important strategic question. If their candidate is a strong contender, does it make sense to bullet vote and only vote for that candidate? In case of voters for a Nader, they have to ask themselves how they relate to more credible choices and how to express that in terms of their voting pattern. Despite the title of Bryan Caplan's book "The Myth of the Rational Voter," I do not think it correct in regards to approval voting to say that voters would be irrational concerning such a choice. Based on this consideration, I am not convinced that voters would elect a Joe Smith about whom they know little.
In the chapter in his book on Gaming the Vote which focuses on Donald Saari and his objection to approval voting, William Poundstone deals a lot with the criticism by Saari that approval voting could lead to the election of a Joe Smith. I have never, for the reasons given above, found this very credible. There has been, as Poundstone briefly alludes to, studies done of this on approval voting in professional societies and data from other elections. As far as I can see, the empirical evidence simply does not give much support to the possibility of a Joe Smith phenomenon. And if it were to occur, I doubt that it would be repeated in subsequent elections.
If it is impossible to have a voting system in which there is no incentive to vote strategically, I would also maintain that it is impossible to avoid a wasted vote in any voting system in the sense that you use the term. If in strategic voting, a voter misreads the polls or they are misleading, a strategic vote may turn out to be a mistake and wasted. If voting for a candidate like Carter turns out to be a mistake for voters as for a number of us in the 1976 election, that vote would also have been wasted. But I would submit that the wasted vote syndrome under plurality voting is of a different order of magnitude which points to one of the great advantages of approval voting.
In talking about voting and fairness in the process the mantra one most often encounters is that of one person, one vote. But both you and I are proponents of voting systems which allows voters more than one vote in an election to a specific office. In this case I think that the appropriate term should be one person, one voice. It is on this score that I have some serious reservations about the Gilson/Hillinger system of approval, neutral, and disapproval voting.
It would be easiest to explain this by starting with the case of instant runoff voting. As Sir Michael Dummett points out in the interview I referred to, IRV has the problem that a small change in preferences can completely change the outcome. As I point out elsewhere, this makes the system of IRV a very manipulable system in that candidates or their supporters can manipulate the outcome by how they rank or advise ranking lesser candidates. The trouble with this is that one group can play around with the preferences of other voters to the disadvantage of the expression of the preferences of another group of voters. I find this an additional troubling aspect of IRV.
But from my perspective, the problem is even worse in the system you and Hillinger advocate. If, to repeat an earlier example, you have an election in which voters vote sincerely for three candidates in which 50% of the voters are indifferent in terms of favoring A or B, 10% favor only B and 40% favor C with half of those casting a negative vote against B, I would argue that in terms of outcome, the election of A over B (50% to 40%) represents a disenfranchisement of at least a minimum of 10% of the voters whose voices were correspondingly annulled. On what grounds can one justify this? How can one evaluate such an outcome in terms of how the results correspond to voters' desires?
If one allows in this scenario for the 10% who favor B to cast corresponding negative votes against A to support their choice, you would get an interesting tie between A (40%), B(40%) and C(40%).
Of course the 10% could also vote against C, which leaves a tie between A (40%) and B (40%) to C's (30%). Given the fact that strategic voting really will take place under any system, I suspect that the incentive for all voters, if they want to protect their voice in terms of expressing their preferences, is to give a negative vote to every candidate to whom they do not give an approval vote.
But on what basis can one judge the efficacy of such outcomes in terms of representing voters' desires? Perhaps if such an approach morphs into what a approval voting election would give, you could say something about the results in terms of evaluating them. Otherwise, I think you have a problem in evaluating how the system operates.
In classical voting theory, the approach, which supporters of range voting reject, to evaluating voting systems is in terms of ordinal analysis--that is in terms of preferences, and not in terms of their intensity. If we cannot determine what intensities of preferences are; as I maintain based on Abba Lerner's reasoning, which I cited in my review of Poundstone's book on Gaming the Vote, is the case; then one must accept that the ordinal approach to assessing the effectiveness of various voting systems in terms of outcomes is the most robust approach to this problem that we can have.