Earlier, I proposed an alternative electoral system called Extended Runoff Voting that some of you took the time to respond to. I would like to take the time to give an update on that as a criticism was brought up by Steve Brams that makes the proposal less desirable than I initially hoped. Extended Runoff Voting appeared to be a bit too complicated to describe in a simple way, so I decided to reformulate the proposal in a way that made it easier to explain without taking away from its objectives. The proposal went something like this:

1. Voters rank the candidates in order of preference. (They are not obligated to rank everyone)

2. First place votes are counted up and if one candidate receives a majority, that person is declared the winner.

3. If however there is no majority, than the candidate with the most first place votes would face off against the candidate with the fewest. Each voters rankings are than reexamined. If a voter ranks the challenger (the candidate with the fewest first place votes) ahead of the contender (the candidate with the most first place votes), than the challenger gets one vote. If a voter ranks the contender ahead of the challenger, the contender gets a vote. (An easy way to start this process is to count all of the first place votes for both of the candidates, than look at the ballots where neither candidate receives a first place vote) The candidate with the most votes defeats the other and the losing candidate is knocked out of the contest.

4. The winner would than face off against the candidate with the second fewest number of first place votes. The winner of that contest would face off against the candidate with the third fewest number of votes and this process would continue until all but one candidate is defeated- that contestant would win the election.

Although I initially believed that the proposal was not a Condorcet method because there was no matrix, it does meet the definitation according to wikipedia which says: ''A Condorcet method is any election method that elects the candidate that would win by majority rule in all pairings against the other candidates, whenever one of the candidates has that property.'' I told Steve Brams that the proposal had the advantage of not being vulnerable to burial or comprimising because of the fact that they are one on one elimination contests. Insincerally burying a potential rival only diminishes the chances of them losing to a more undesirable candidate. Strategically ranking a lesser evil ahead of your prefered candidate no more helps you defeat the greater evil than voting sincerally.

Brams gave the following reply:

Dear Jarrett,

You're quite right--I got things reversed (a senior moment, I suppose). So let me change my example slightly by interchanging b and d in the 2 cabd voters' preferences to cadb:

4*: a d b c

3: b d c a

2: c a d b

* number of voters

a faces off against d (0 first-place votes), and a knocks him out by 6-3. Now we have

4: a b c

3: b c a

2: c a b

a faces off against c, and c knocks him out by 5-4. Now we have

4: b c

3: b c

2: c b

so b wins by 7-2 (though a can beat b by 6-3).

Now let's assume that the 2 cadb voters who rank b last don't show up, giving

4: a d b c

3: b d c a

a faces off against c and then d (the order doesn't matter), who each get 0 first-place votes, and a knocks each out by 4-3. Now we have

4: a b

3: b a

so a wins by 4-3. Thus, b wins when the 2 cadb voters who rank him last show up but loses when they don't.

This is the no-show paradox as Fishburn and I defined it in our 1983 Mathematics Magazine article: "The addition of identical ballots with candidate x ranked last may change the winner from another candidate to x." See p. 207 of

http://www.jstor.org/stable/2689808

Specifically in my example, the addition of 2 ballots with candidate b ranked last (cadb) changes the winner from a to b. That is, nonsupporters can help a candidate win under your system.

Best wishes,

Steve

It seems that in all likelihood that both systems are vulnerable to the no show paradox unfortunately, which is probably the most notable problem. I find the failure of the participatory criteria to be very bizarre and would not have believed that any system could fail this criteria unless it was shown to me. So approval voting, asset and SODA are looking like acceptable alternatives for single winner elections.

Sincerely,

Jarrett Gabriel