Voting Methods and Electronic Voting

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Voting Methods and Electronic Voting

Postby bobk » Wed Oct 03, 2012 9:48 am

I recall a discussion about possibly having electronic voting for the club, so I wanted to share some of my experience in researching voting methods for the HGAA. JB was involved in some of these discussions and he's welcome to chime in if he's on the forum.

The HGAA had a big debate about various voting methods (some good ... some horrible), and I spent a fair amount of time researching various systems like "Instant Run-Off", "Condorcet", and "Range Voting". It turns out that one of the big problems with Instant Run-Off is that "consensus" candidates (those who are acceptable to a large majority) can be eliminated in the early rounds because they are ranked below each "factional" candidate on each voter's ballot. For example, if you have 6 candidates (5 "factional" and 1 "consensus"), you might find that each of the 5 "factional" candidates were ranked highest by the 20% of the voters who backed them, and that no one (or very few) ranked the 6th "consensus" candidate highest. So the "consensus" candidate would be eliminated in the first round even though they might have been the second choice on everyone's ballot. Here's an example assuming candidate "A" is the "consensus" candidate and B,C,D,E,F are "factional" candidates:

20 Ballots marked: B, A, C, D, E, F
20 Ballots marked: C, A, B, D, E, F
20 Ballots marked: D, A, B, C, E, F
20 Ballots marked: E, A, B, C, D, F
20 Ballots marked: F, A, B, C, D, E

In that case, the consensus candidate "A" would be removed in the first round using "Instant Run Off". But ask what would happen if candidate "A" were to really have a "run off" against each of the other candidates in a true one-on-one race. Here's what you'd find according to the ballot preferences above:

Candidate A would defeat Candidate B by 80 to 20
Candidate A would defeat Candidate C by 80 to 20
Candidate A would defeat Candidate D by 80 to 20
Candidate A would defeat Candidate E by 80 to 20
Candidate A would defeat Candidate F by 80 to 20

In other words, Candidate A would "clobber" all others by a factor of 4 to 1!!! So why did A lose under "Instant Run-Off"? The answer is that Instant run-off makes its decisions by only looking at the "surface" of the votes. It only looks at the FIRST choice by each voter and ignores all the information contained "below the surface". In this example, that would lead to a victory by a candidate with only 20% support.

So is there a better system? Yes. The Condorcet criteria states that the winner should be the one candidate who would beat all others in a one-on-one basis (if such a candidate exists). The parenthetical clause is needed because it is possible to have a "Rock, Paper, Scissors" case where A beats B, and B beats C, and C beats A. There are complicated ways of attempting to apply the Condorcet criteria to those cases, but then it's not so simple for people to follow what's being done. My proposed solution in those degenerate cases would be to simply apply another criteria (like traditional Instant Run-Off, or Range) as a "tie breaker".

Again, this post is primarily to share my experience with various voting systems in case the club should decide to adopt either electronic voting or "multiple candidate" voting any time in the future.
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