APPENDIX 1: RANGE VOTING FURTHER CLARIFICATION

 

 

                                                      APPENDIX 1

 

                                  RANGE VOTING FURTHER CLARIFICATION

 

The following was written after I came across the piece by Balinski and Laraki on "Elections by Majority Judgement."  That article was helpful in clarifying my understanding of range voting.  As a result, I wrote the following to lay out how I now view the issues concerning the range vote approach to elections.

 

                                              October 29, 2009

 

       THE RANGE VOTING APPROACH TO ELECTIONS: MY RESERVATIONS

 

Range voting is a voting system under which each voter evaluates every candidate on some scale such as 1 to 5, 1 to 10, etc., with the candidate having, subject to a reasonable constraint, the highest numerical or average score winning.  While I have learned a lot from advocates of the system, I have strong reservations about their methodological approach to analyzing voting systems and about their conclusions.

 

The purpose of this note is to briefly set these reservations out by doing three things: First, by explaining my understanding of the basic arguments that range voting advocates make.  Second, by outlining my objections to these.  And finally, briefly summarizing an alternative approach, which came to my attention, to elections with a range vote flavor that avoids the problems discussed below.  In doing this, I start with the example of a two candidate election with 100 voters in which 52 favor candidate A and 48 B.

 

In such an election, if the voters assign scores on a 1 to 5 scale and the 52 voters assign 3s and 1s to A and B respectively and the 48 1s and 3s to A and B also, we get an average score of 2.04 for A and 1.96 for B, the same result as in a regular election where A beats B 52% to 48%.  But if half of the 48 give B a score of 5 instead, we get an average score of 2.44 for B as opposed to 2.04 and B wins.  The question naturally arises in this case as to why should their voice count for more and change the outcome.

 

The range vote advocates' answer to this question is that such an outcome reduces or minimizes what Warren Smith labels "bayesian regret" or "expected avoidable human unhappiness."  That is this alternative outcome results in the greatest overall satisfaction for voters.  But this implies interpersonal utility comparisons and it is my understanding that in his bayesian regret simulations of voting systems Warren Smith assigns utilities to virtual voters.

 

Here we run into three difficulties.  In the first instance, we have no way of making interpersonal utility comparisons to arrive at some measure of overall satisfaction with election results.  Any supporter of A could credibly claim that his or her welfare (utility) loss was greater than the welfare gain of any supporters of B in the situation where B wins and we have no means of refuting or disproving it.  This is the same dilemma that many economists encounter in their work with the concept of utility.  This has led them to conclude that the idea of measuring based on utility total satisfaction for society is unscientific or illogical.

 

Another problem which arises here is that of scale norming.  Scale norming arises in elections when for subjectively the same evaluation of a candidate voters assign different numerical values on the scale used.  Aside from an arbitrary assignment of scale norming in simulations, we have no way of determining its magnitude as well in a range voting system.

 

Finally, from the voting results itself, we have no way of distinguishing between sincere and strategic voting patterns.  It could be in a subsequent election between A and B with our 100 voters that all of A's supporters assign a score of 5 to their candidate assuring his or her win.  But how one can distinguish from the voting date the extent to which this is due to a sincere shift in preferences or to strategic voting is totally unclear.

 

Given these considerations, it is difficult to see how computer simulations based on assigned utilities to virtual voters can be a valid basis for analyzing different voting systems.

 

In response to this objection, the assertion has been made that the issue is not one of utility comparisons but of probabilities.  That is, the simulations show that range voting has a greater probability of maximizing voter satisfaction of its outcomes than alternative voting systems.  But how one can have statistical or any probabilities without measurable or countable units is totally unclear.  On this score, it is hard not to conclude that range voting supporters'

simulations based upon utilities assigned to virtual voters represents a self-contained system that assumes what it purports to demonstrate.

 

If we could make interpersonal utility comparisons, the criterion for judging voting systems suggested by the proponents of range voting would make a lot of sense.  But since we cannot, one needs some other criterion or criteria for judging the effectiveness of alternative voting systems.  In pointing this out, there may be something to learn from the traditional economics approach to utility/welfare analysis.

 

In that approach, while economists eschew value (interpersonal

utility) comparisons, they do use monetary comparisons (price measures as opposed to value measures) to come to robust, important conclusions in areas like welfare economics, industrial organization and trade theory.  The concepts of consumer and producer surplus from microeconomics underly such analysis.  I see no reason why voting analysis should not follow a similar pattern.  The real issue here is what would be an equivalent approach in voting analysis.

 

The paper by Michel Balinski and Rida Laraki on "Election by Majority

Judgement: Experimental Evidence" is an example of an approach to analyzing voting systems of a range voting flavor which avoids the pitfalls of the range utilitarian approach.  Instead of using numerical values as on a scale of 1 to 5, Balinski and Laraki propose using descriptive words like great, good, fair, poor, bad and reject to evaluate each candidate.  Based on these, they calculate median scores for each candidate which are then used to rank the candidates in terms of their descriptive scores and determine a winner.  They, rightly, it seems to me, label their voting system as ordinal in its approach.  And indeed their analysis of results of their voting system follows what seems to me to be the traditional ordinal approach to voting theory in using polling data and the like.

 

Until I encountered range voting, all the approaches I had seen on voting theory followed what I would describe as an ordinal approach.

Because of the problem of making interpersonal utility comparisons, this makes a great deal of sense to me.  Due to this problem, an ordinal analysis of voting systems is surely more robust than a cardinal analysis.  Those of a range voting persuasion need to take this into account in their analysis and simulations of voting systems if they wish to come up with credible and useful conclusions.