Week 6: Borda Count and Range Voting

Welcome to Week 6 of "The Mathematics and Implementation of Election Theory." This past week, I have been quite productive, so I can't wait to share everything I've discovered thus far.

BORDA COUNT:

Borda Count was developed as early as 1435 by Nicholas of Cusa to elect Holy Roman Empires but formally proposed in 1770 and named after French mathematician and political scientist Jean Charles de Borda. In this method, each candidate on a preference list is assigned a specific number of points that corresponds to his or her position on the list. Different regions and elections utilize different point systems; typically, though, in a "pure" Borda Count system, the first-choice candidate in a preference list is given "n" points, the second-choice is given "n-1" points, the third choice "n-2" points, and the last choice is given 1 point. However, there is a slightly revised version of this: the first-choice candidate is given "n-1" points and the last-choice candidate doesn't receive any points.

And in places such as Nauru, a country in Micronesia, voters must list every candidate, and the points do not descend in uniform steps. Rather, they use a logarithmic scale: the first-choice gets 1 point, the second-choice gets 0.5 points, the third choice gets 0.3 points, then 0.25, 0.2 etc. until it gets to 0.1 points. This version places a particular emphasis on the candidates at the top of voters' lists, which makes sense, as this was also a particular concern that was discussed in the survey I sent out earlier in the month. Several of the people who filled out the survey said that voters tend to be very passionate about their feelings about their favorite and least favorite couple of candidates, and the ones in middle tend to be pretty nebulous in voters' minds.

I did find, though, that for the logarithmic method utilized in Nauru, it is much more likely for a dominant major candidate to win than one that is broadly liked. Let me explain. Suppose we have an election with five candidates and 140 voters (see image for the preference profile).

In Nauru, the winner would be Candidate A, but Candidate would be the "pure" Condorcet winner. We run problems similar to those of plurality, which is unfortunate, as in my mind, electoral systems should really take into account every voter's thoughts about every candidate.

Borda count is also utilized to elect two ethic minorities (those from Italy and Hungary) to the National Assembly of Slovenia and in the parliament of the island nation Kiribati to decide presidential candidates.

RANGE VOTING:

Range voting is a system that falls under the umbrella of "cardinal voting," in which voters give candidates independent ratings. In range voting, voters are required to give the candidates a rating, usually from 1-5 or 0-9, which represents how much the voter likes/supports the candidate, with the lower number being equivalent to a lower rating. At first, I thought that this was a pretty arbitrary voting system, but when I thought about it a little more, I realize that we apply versions of range voting in our daily lives; for example, rating movies or giving scores in figure skating and diving competitions, and these ratings, when all taken together, seem to be relatively trustworthy. However, I do acknowledge that the larger the range, the higher the chance of an "exaggerated vote," or vote manipulation.

That is it for this week! I did a bit of the Condorcet method, but I'll go more in-depth into that in next week's blog post, because I am turning in a paper next Friday on Borda count, range voting, and Condorcet.

See you next week!