# Range Voting

Range Voting is a method of assigning points to all the candidates and then adding up the points garnered by each candidate with the winner being the one with the largest point total. Or, alternatively, the average may be computed and the one with the highest average wins. Range Voting is a modified Borda Count in which the maximum and minimum point assigments remain fixed regardless of the number of candidates running. In the Borda count the maximum point assigment is equal to the number of candidates minus one (assuming the minimum point assignment is 0). Also Borda does not allow for the same number of points to be given to multiple individuals. I came up with this method independently and called it the"Lawrence Count," but I said on this web page that it "seems so obvious that maybe someone has already discovered it. If so, I relinquish the name and any claim to being its progenitor." Another chap by the name of Warren D. Smith has come up with a similar system called range voting which is essentially the same thing as the modified Borda Count. I assume he is the one who named it "range voting," although there may have been other progenitors as well.

With the Borda Count the rank and hence the maximum number of points that can be assigned to a candidate is determined by the number of candidates. For instance, if there are 5 candidates, 4 points are assigned to first place, 3 to second and so on, 0 to last. Range Voting differs from the Borda Count in two ways: 1) the number of places does not have to equal the number of candidates; and 2) more than one candidate can occupy a particular place. Range Voting lends itself to the digitalization of the vote since, if there are N places and n candidates, each voter submits log 2 N bits of information regarding each of the n candidates. Since votes will undoubtedly be tallied by means of supercomputer, it would be helpful if N were a power of 2. The higher the value of N, the greater the freedom of expression for each voter which is limited, ultimately, by an individual’s ability to discriminate between 2 candidates. If a voter can’t decide if he prefers one candidate to another, then there is no use in increasing N in order to give him or her additional levels of “sensitivity.” As long as N is the same for each voter, each voter will be able to specify the same amount of information with regard to each candidate and the same amount of information over-all. Therefore, each voter has an equal vote. Please see my paper, "Social Choice, Information Theory and the Borda Count". See Figures for "Social Choice, Information Theory and the Borda Count."

For example, let us assume that there are 4 candidates A, B, C and D, 3 voters and 8 places. Then each voter would specify 3 bits of information regarding each candidate as follows:

 Voter 1: Voter 2: Voter 3: A 011 A 001 A 010 B 111 B 000 B 010 C 000 C 100 C 101 D 011 D 111 D 011

The possible votes are 000 (0), 001 (1), 010 (2), 011 (3), 100 (4), 101 (5), 110 (6), 111 (7) for those who are not conversant with binary numbers.

The total for A would be 6; B, 9; C, 9; D, 13. So D would be the winner. Notice that there are no anomalies (as there are in the Borda Count) if one candidate drops out. The totals for the other candidates are not affected although I’m a firm believer that when the candidate list changes, the voters should be repolled. Please see my paper, "Social Choice, Information Theory and the Borda Count". See Figures for "Social Choice, Information Theory and the Borda Count." Also not every place need be filled by any particular voter as in the Borda Count, and a voter may rank more than one candidate in the same place. That would indicate that the voter is indifferent among the candidates so ranked or in other words those candidates are tied in the voter’s preference list.

Much has been made of the fact that the Borda Count is open to “insincere voting” or “manipulation” or “strategic voting.” I’d rather consider that a voter may vote strategically which is his or her privilege rather than “insincerely” or “manipulatively” which are pejorative terms. With Range Voting a voter could vote strategically as follows. Say that before the final vote the race had narrowed to just 2 candidates. Then every voter could give the highest place to his favorite of the 2 and the lowest place to his least preferred of the 2. The maximum spread between the candidates will affect the outcome the most. What is wrong with that? I say nothing. A voter voting this way is taking his chances for the following reasons. First, he will not have certain knowledge that the race has narrowed to just 2 candidates. Therefore, he will be taking a risk. For example, let us say that the race has narrowed to just A and B, and a voter prefers A to B but there are other candidates that are less preferred than B. Therefore, if the voter places B last, he is taking the chance that one of those candidates less preferred than B will actually win (since he will be ranking them higher than B). Likewise, by ranking A first when there are candidates more preferred than A, he will be taking the chance that one of these would have won if he had ranked A below them. Finally, if he is relatively indifferent between A and B, it wouldn’t be worth taking the chance that, by voting strategically, one of them might not win. If he is polarized between A and B, he is going to want to put the greatest spread between them anyway without any consideration of voting strategically.

Another strategy would be to give A and everyone ranked above him the highest rating and B and everyone ranked below him the lowest rating. Then the question is what to do with the candidates ranked between A and B. It might be best just to rate them "honestly" irrespective of the other candidates with A and B being the two poles.