Statement by Forest W. Simmons about voting methods

Including his suggested standard ways to use range voting with other kinds of ballots

This page was written by Forest W. Simmons, with a small amount of post-editing by WDS. Simmons has been one of the most active and influential workers on the "election methods" internet archives.

I favor range voting – with various standard conversion methods (discussed below) for converting non-range-style ballots to range format.

I have been teaching mathematics at the college level since 1977. When first faced with giving partial credit to students I looked for an objective way of doing it, by ranking all of the students' efforts on each problem, and then combining the rankings by the Borda count, etc.

That didn't work very well. So I ended up trading the Borda Count for range voting, i.e. assigning each student a number in the range from zero to one as credit or partial credit for each problem.

In this analogy the students (candidates) are judged by their performance on the various problems (voters). [My initial post on the EM listserv more than five years ago was based on this analogy.]

When I read Saari's book Geometry of Voting, I noticed that he made implicit use of Cardinal Ratings (range voting) to compare the Borda Count with other methods. I wondered why not use CR as a method instead of just a standard of comparison?

When I posed that question to various people, they all came up with the standard reasons... it's easier to rank than to rate, one person's rating means something different than another's so they shouldn't be additive, etc.

But these objections were counter to my many years of experience with grading papers. Personally I find rating easier than ranking, and in the case of voting we don't have to worry about how much to weigh a problem (i.e. ballot) because each vote should have the same weight, unlike math problems, some of which are more important than others.

Students get their grades from various kinds of teachers, but their grade point averages are calculated additively.

However, I saw the value of Approval Voting as a simple approximation to CR, analogous to rounding partial credit to zero or one. In the long run (i.e. in a large electorate with many papers being graded for each student) the statistics of rounding yield the same result with near certainty. However, in voting there is a psychological value to not requiring the rounding.

My compromise is "range voting with options." Those who want can vote the full range ballot. Those who want to round can vote an approval-style ballot. Those who prefer to rank can do that. Those who want to rank with an approval threshold, can do that. And those who want to vote "above the line" can do that by marking a party or candidate. "Above the line" voting has been used in Australia. In Australia, ballots are rank-order ballots totalled by single-transferable vote methods. Voters who do not wish to specify a full rank order, can instead simply name a political party, and then the rank-ordering pre-specified by that party (these are worked out in inter-party deals, and published, before the election) is employed.

All of these ballots are automatically converted to range ballots for the final tally. The candidate with the highest average rating wins.

The most interesting conversion is ranked-with-approval-cutoff→range:

The approval cutoff is placed at midrange. The candidates are spaced as evenly as possible in the given range consistent with the preservation of the ranking order and the cutoff being placed at midrange.
So if the range is zero to 100, the ranked ballot A>B>threshold>C>D>E>F yields the respective ratings of
100, 75, 50, 37.5, 25, 12.5, and 0
Note that "threshold" automatically has an average rating of 50.

The other conversions are straightforward: rankings are converted by evenly spacing (e.g. A>B>C converts to 100, 50, and 0); "above the line" party-voting is the same except the pre-established rank-order vote pre-published by that party is used; (one could also imagine allowing parties to pre-specify range-type votes, but so far that idea has never been employed in national elections); and approval ballots are converted by approved=100, disapproved=0.

If no flesh and blood candidate has an average rating higher than threshold, then the term of the winner should be shortened.

The "above the line" option that is heavily used in Australia gave me the idea of several versions of W.D.Smith's "Asset Voting" that I called (variously) "Candidate Proxy" and "Candidate Transfer." Warren Smith discovered his versions independently not long after.

For electorates that don't want to deal with any ballots other than Plurality style ballots, I recommend some version of Asset Voting or Delegable Proxy that uses only Plurality ballots.

My interest in pairwise and non-deterministic methods have to do with trying to remove the strategic incentive for voting near the extremes in range voting. "Random Ballot" accomplishes this but at a cost of giving even the candidates with nearly zero average ratings chances of winning. That's a thorny problem that may have no nice solution.

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