CHAPTER 8


                                    A GREAT BOOK ON VOTING SYSTEMS

                                                 WITH A SERIOUS FLAW


Although William Poundstone's book on "Gaming the Vote" is a great source for understanding the issues of voting systems, I have serious reservations about its position on range voting.  The following review sets out my reservations on this in more detail than in the introductory and preceding chapters.  The citations to this review may also serve as a useful guide for those who might be interested in further readings on the issues discussed here.



                                           April 14, 2008




By John Howard Wilhelm


William Poundstone

Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) Hill and Wang, 338 pp., $25.00


It surely is clear that a vast majority of Americans realize that our political system has badly broken down as witnessed by the excessive partisanship which has come to characterize our two-party system of governance.  In response to this, a number of remedies have been proposed none of which seem to work or really promise to do so.


The most often used approach is a call to "throw the bums out."  In the early 1990s, Jack Gargan, the ousted chairman of the Reform Party, organized his THRO CAMPAIGN which by his and other accounts in 1992 "was mainly responsible for electing 124 new faces to Congress, a number that was FAR more than in any election year since Depression days!"  The problem, as we all know, was that this opened the House of Representatives up to a Republican takeover after the 1994 election and more, not less, partisanship under the new House leader Newt Gingrich.


An element of Gargan's campaign that has also been tried is term limits.  Under the influence of such pressures the State of Michigan instituted term limits for members of its State Legislature.

Unfortunately, this remedy, as more and more people in Michigan are coming to realize, does not work too well either.  It leads to the loss of an important asset for a legislature, institutional memory, and increased legislative gridlock on pressing state matters such as solving a state's fiscal crisis.


Another approach is for conscientious voters to make an effort to elect an honest, well-intentioned politician to political office.

Unfortunately once again this also may not work so well as a number of us who voted for Jimmy Carter in the 1976 election learned to our chagrin.  Many national political candidates argue, as Barack Obama currently does, that the solution lies in electing people of goodwill to our highest national offices.  The problem with this is that such goodwill had and does nothing to change the incentives under which our politicians currently operate nor the system under which they are elected.


The issue here, which is not discussed by our major candidates and parties, is: How to break the political duopoly which our increasingly dysfunctional major parties enjoy in order to open up our political processed to other groups and individuals?  For those of us who believe that voting reform is the key to this, two recent events are encouraging.


Each year in April Mathematics Awareness Month, cosponsored by the American Mathematical Society, American Statistical Association, Mathematical Association of America and Society for Industrial and Applied Mathematics, is held.  This year's theme is on Math and Voting.  One of the sponsors, the AMS, to its credit published some time ago a good college primer on the Mathematics of Voting and Elections [1].  Given the fact that mathematicians have done interesting work on voting theory, the emphasis this year on math and voting is not only relevant, but also much welcomed.


The second very encouraging event is the recent publication of William Poundstone's book on Gaming the Vote which is simply an excellent source for understanding the issues here.


                                                  POUNDSTONE'S BOOK


Many believe that it is our electoral college system that is a major impediment to better elections, especially at the presidential level.

Poundstone does an excellent job of dispelling this notion.  Even if we replaced the electoral college, which we could easily do by an interstate compact allocating electoral votes to the candidate with the most votes, we would still be stuck in multi-candidate elections like 1992 with the "worst voting system"--plurality voting.


Pundstone uses the 1983 Louisiana governor's election and the later

1991 governor's election in that state to illustrate the pernicious consequences of plurality voting where voters have only one vote each to cast in multi-candidate elections.  He goes on to document convincingly that this has been a repeated problem throughout American history whenever "vote splitting," or the spoiler role of third party or independent candidates, arises.


In addition to pointing this out, Poundstone goes on to show how increasingly our major parties are using splinter candidates to manipulate election outcomes in their favor.  The most obvious example of this was the Republican support for Nader's efforts at ballot access in 2004 and Democratic dirty tricks to deny him such access.


Poundstone does a good job in his book of relating to the reader the history of the technical issues of voting theory beginning with Condorcet and Borda in the 18th Century, continuing with Charles Dodgson (Louis Carroll) in the 19th Century right through the late 20th and early 21st Centuries.  In discussing the current state in this area he spends considerable time relating in a useful and very competent manner the important players in the current debate: Steven J. Brams, Donald G. Saari, Warren D. Smith and Claude Hillinger.


For a person like myself, with an amateur interest and some knowledge in this area, it impressed me a great deal when Poundstone characterized Clay Shentrup, a supporter of range voting, "as one of the most militant figures in voting reform."  Based on my own experience with proponents of range voting like Smith and Shentrup, I can see that Pounstone knows the area he is dealing with very well.

If I had to make a guess on how intelligent laymen should rate a book like this on a scale of 1 to 5, I would suggest an average rating much closer to a 5 than a 4.


I first got interested in the area of voting theory when I encountered Steven J. Brams's and Peter C. Fishburn's 1983 book on "Approval Voting" which is now available in a second edition with a new preface [2].  As I became more interested in this area, I acquired materials like the AMS's book on the mathematics of voting for non-mathematical college majors and Donald Saari's book "Decisions and elections:

Explaining the unexpected" [3].  It has been difficult for me to understand Saari, but Poundstone's exposition on him helps a great deal on this.  Steven Brams new book on Mathematics and Democracy [4] looks to be an interesting read.


The advantage of Poundstone's book is that it makes much of this type of material available to the concerned citizen in clear prose.  My disagreement with Poundstone is on his seeming preference for introducing range voting over approval voting in our national elections.


                                     THE CASE FOR APPROVAL VOTING


Approval voting is, as Poundstone pointed out to me in an e-mail exchange, by "far the least complicated [voting system] next to plurality."  Under approval voting in a multi-candidate election a voter can give one vote each to the candidate or candidates he or she approves of with the candidate having the most votes winning.

Approval voting is, according to the advocates of range voting, a special case of the latter in which the rankings under AV is either 1 or 0.


Under range voting, a voter can give a ranking on a scale of 1 to 5, 1 to 10 or 1-100 to each candidate in a multi-candidate election with the candidate with the highest score or highest average score winning.


My interest in approval voting began with concerns I had about reform in the former Soviet Union.  In July 1991 in Moscow, I gave a talk in Russian to members of a small working group in the Academy of Sciences.  In that talk I advocated using a variant of approval voting to elect a constituent assembly to sort out the country's problems and establish a new political dispensation.  The variant of an approval voting election that I proposed would have constrained the maximum number of members of the KPSS elected to the assembly to no more than 24% of the total delegates.  I thought then, and think now, that such a limitation was essential for a better outcome than we got or could otherwise get.


After the 1992 election, I concluded that our country badly needed to open up its political processes to responsible third parties.  In thinking about this, I concluded that the introduction of approval voting in our elections was probably the best way to achieve this.  In June 1996 I wrote an unanswered letter to Ross Perot urging him not to run but to use his political visibility to push for introducing approval voting in our national elections.  After the 1996 election I tried to reach Jessie Ventura on this issue.  Although I had advice and help from former Governor Richard Lamm of Colorado, I simply was unable to get through the people around Venture to engage him on the issue.


For a number of years after, I engaged in a personal effort to educate members of the Green and Reform Party movements about approval voting and the inadequacies of instant-runoff voting.  I had not known nor heard anything about range voting prior to the summer of 2007 when at the suggestion of Richard Winger, publisher of Ballot Access News, I contacted Clay Shentrup.  Winger knew of my advocacy of approval voting over instant-runoff voting and suggested my talking with Shentrup because he knew that Clay shared similar views.


While instant-runoff voting (IRV) may be an improvement over plurality voting it is as Poundstone makes clear in his book, a bad choice among the alternatives available to that system.  As Professor Steven Brams pointed out in a talk sponsored by the University of Michigan Mathematics Department in November 2005, the advocates of IRV frequently do not understand how that system of voting actually operates.  This is a point on which Clay Shentrup and others in the range voting movement are correct, something that Rob Richie and others associated with the Center for Voting and Democracy like John Anderson apparently do not understand.


While I agree with the proponents of range voting on the issue of IRV, I don't agree with them and Poundstone on the superiority of RV over AV on practical and methodological grounds.


One advantage which AV has over RV is, as Poundstone pointed out, that it is a much simpler system.  It is also a much more transparent system in terms of understanding election outcomes.  If a winning candidate has a certain approval rate such as a 51% of the votes cast under this system it tells voters something concrete that they can understand in terms of how we normally, and sensibly, view support levels.  That is certainly not the case with RV as winning scores or averages in of themselves convey little about support levels as they are normally understood in elections.


Jan Kok maintains, according to Poundstone, that range voting like approval voting can be run on every voting machine presently in use in America.  While it is true that there are serious problems in adopting a ranking system like IRV given our current voting infrastructure, I find it hard to believe that a system like RV is just as easy to integrate into our voting system today as AV would be since the latter just entails nothing more that additional counting.


It is my contention that range voting looks a lot like utility theory in microeconomics where we use the concept of utility to explore the basic logic of consumer behavior in the market place.  But there is one major problem with this: We have no way of comparing interpersonal utility.  This basically limits welfare comparisons to the idea of the Pareto optimum where we in essence use the opportunity cost of money to make comparisons between alternative situations and their social desirability.  We don't use utility in the benthemite sense of the greatest good for the greatest number because we have no way short of subjective evaluation of making such a comparison.


The approach of the proponents of range voting to this issue is quite different.  As Poundstone points out in his book, Warren Smith, the main proponent of range voting, "tried to gauge how voting systems fail the voters by electing candidates other than the one who would have resulted in the greatest overall satisfaction.  To do this, he ran a large series of computer simulations of elections.  In each of his simulations, virtual voters were assigned utilities (degrees of happiness, measured numerically) for simulated candidates."


When I objected on economic grounds to this approach, I was referred by the supporters of range voting to an article on "Utilitarian voting"

by Professor Claude Hillinger which is cited in the sources, or bibliography, of Poundstone's book.  The problem I have with the article is that it is a polemical, rather than an analytical, piece.


Both Hillinger and Warren Smith refer to Lionel Robbins and his influential book on economic methodology [5] as the major source, from their view, of the "economic orthodoxy" in the last century that interpersonal comparisons of utility are impossible.  Hillinger ties this into the conflict between orthodox economics and socialism in the last century.  As Hillinger put the issue, "Robbins reasserted the marginalist position that there was no scientific basis for the measurement of utility, and hence no basis for the socialist position that one could have scientific, and hence 'value-free,' policies that would maximize the aggregate welfare."  He cites happiness research as a contemporary example of a break with the "orthodox" economic tradition on this issue.


Hollinger's implication that this issue was one of just orthodox economists versus those on the left interested in applying scientific principles to achieving desirable social goals is simply not justified by the facts.  There certainly were economists on the left interested in this issue who clearly accepted and understood the "orthodox"

position on interpersonal utility comparisons.  As examples I would cite Oskar Lange and Abba P. Lerner.


Abba Lerner in his classical book on The Economics of Control [6] carefully outlines in his third chapter dealing with the optimum division of income the conditions necessary for achieving a benthemite state of the greatest good for the greatest number in terms of income distribution.  He then goes on to make a statement that is worth quoting in detail in terms of understanding the issue here.  It is as follows:


[Here we come up against a serious difficulty.  Our assumptions that individuals are capable of feeling satisfactions and that their satisfactions are of the same kind of thing have given meaning to the concept of maximizing total satisfaction, while the principle of diminishing marginal utility of income has simplified the task to one of equalizing the marginal utilities of income to all the individuals in the society.  But we have no means of doing this.  There is no way of discovering with certainty whether any individual's marginal utility of income is greater than, equal to, or less than that of any other individual.]


[If any two individuals were know to have exactly the same capacity of distilling satisfaction out of income, it would also be known that an unequal division of income between them would make the marginal utility of the larger income less than the marginal utility of the smaller income and that an equalization of income would equalize their marginal utilities and maximize the total utility enjoyed by both together.  If it were known that one had a greater capacity for satisfaction (at all income levels), it would also be known that an equal division of income would result in a greater marginal utility of income for the one with the greater capacity for satisfaction, so that it would require an unequal division of income, more going to the one with a greater capacity for satisfaction and less going to the one with a smaller capacity for satisfaction, to equalize the marginal utilities of income and maximize the total satisfaction.  But these things are not capable of being discovered.  Every individual could declare that he has exceptionally high capacities for satisfaction and so should be given more income than anybody else if total satisfaction is to be maximized; and there is no way of testing the validity of such a claim.] [7]


Clearly such claims, as Kennith Boulding pointed out in a class I took with him years ago, are plausible.  The problem here in terms of the issue of the validity of interpersonal utility comparisons is that there is no way to refute the validity of such claims.  In other words, interpersonal utility comparisons aren't scientific because they are "not even gnorw."


This seems hard for Warren D. Smith and the proponents of range voting to accept.  But aside from this there is a problem that I believe that they overlook.  The problem is that even if people can scale their assessment of a candidates on a consistent basis, it does not follow that they can avoid scale norming among themselves.  As Daniel Haybron has pointed out in a recent article dealing with some of the conceptual problems of happiness research [8], scale norming presents serious problems here because one person's ten might be another's six for a similar subjective evaluation of a candidate.  Scale norming is clearly a ubiquitous social phenomenon. Grading is a clear example of this which is why we resort to standardized tests to try to measure things in that area more accurately.  The upshot of this is that one cannot rule out a fallacy of composition in computing total scores for candidates in elections.  That is, while individual scales may at least be clear to each person, the aggregate results can vary quite widely depending on how troublesome scale norming is, something which in elections the size of those for president or members of congress surely limits the confidence one can have in the outcome irrespective of computer simulations based on an assumption of interpersonal utility comparisons.  This surely makes the problem of transparency much more acute for a voting system based on cardinal rather than on the ordinal considerations which characterize our plurality voting system and a system like approval voting.


If opening up our political processes to third parties is what is needed to improve the functioning of our political system and we need to do it now, I would argue based on these considerations that approval voting is at present the best way to go.  As far as I can see, it could even easily be introduced in this election cycle.  It is a simple and transparent system that would clearly get rid of the wasted vote syndrome.  The issue though is what can be done and how can we do it?




In his book Poundstone points out that Brams has done some research and has concluded that approval voting does not violate any state constitution.

That is it would only require a statutory act to put it into force.  But Poundstone does not deal with the issue of whether this is possible in federal elections and if so how we might go about getting this.


Given the requirements of the Constitution, Article I, Section 4 and the 14th Amendment, and the precedent in Oregon v. Mitchell in a 1970 Supreme Court decision, it is clear that AV can be mandated in federal elections by a simple federal statutory act.  Or as Justice Black writing for the Court in Oregon v. Mitchell (1970) put it:


     I would hold, as have a long line of decisions in this Court,

     that Congress has ultimate supervisory power over congressional

     elections.  Similarly, it is the prerogative of Congress to

     oversee the conduct of presidential and vice-presidential

     elections and to set the qualifications for voting for electors

     for those offices.  It cannot be seriously contended that

     Congress has less power over the conduct of presidential

     elections than it has over congressional elections.


Such an act should do three things:  1) Mandate approval voting in all federal elections, 2) Mandate a place on the federal ballot for five political parties, four occupied by the four top parties in terms of number of votes cast and the fifth position filled by a nation wide competition open to other parties and groups, and 3) Give congressional approval for an interstate compact to allow the allocation of state electors to the candidate with the most popular votes as long as that candidate has at least a 50% approval rate.


Three things can bring this about.  First, we need to have a public discussion on how to improve our political processed, including our elections, to improve the operation of our political system.  The merit of Poundstone's book on Gaming the Vote is that it makes a significant contribution to such a discussion.  Second, those wishing for real changes in our political processes need to organize a petition now to Congress for the voting reform the country sorely needs.  And third, the electorate ought to make it clear that they will not support any Democrat or Republican in the next election who cannot support a better voting system for the people to express their preferences in elections and open up our political processes to responsible third parties and to more independent individuals.




1.  Hodge, Jonathan K.; Klima, Richard E. The mathematics of voting and elections: A hands-on approach.  Mathematical World, 22 American Mathematical Society, Providence, RI, 2005, xiv + 226 pp.


2.  Brams, Steven J.; Fishburn, Peter C. Approval voting. Second edition, Springer, New York, 2007, xxii + 199pp.


3.  Saari, Donald G. Decisions and elections: Explaining the unexpected. Cambridge University Press, Cambridge, 2002, xiv + 240 pp.


4.  Brams, Steven J.  Mathematics and democracy: Designing better voting and fair-division procedures.  Princeton University Press, 2008, xvi + 362 pp.  $27.95


5.  Robbins, L (1932), An Essay on the Nature and Significance of Economic Science, London, Macmillian. Third ed., 1984, New York University Press


6.  Lerner, Abba P. The economics of control: Principles of welfare economics.  The Macmillian Co., 1944, New York, xxii + 428 pp.


7.  Ibid., pp. 28-29


8.  Haybron, Daniel, "Do We Know How Happy We Are?  On Some Limits of Affective Introspection and Recall," Nous, Vol. 41, No 3, 2007, pp. 349-428.