[EM] IRV done right... satisfies Strong FBC?

Antonio Oneala watermark0n at yahoo.com
Tue Mar 28 11:31:29 PST 2006

Whenever I came up with this election method, which I think I will call Transferrable Approval Voting, I was thinking about the problem of strategic voting in approval.  The thing is, that if everyone votes perfectly strategically, then the best candidate is usually gotten.  The problem with normal approval is that it is later-no-harm... by ranking a candidate you could possibly hurt the candidate you already have ranked.  So the strategy is to approve of as many of your favorite candidates as possible without contributing to your candidate losing.  It's almost impossible to do this in one election.

So, why not simply allow people to provide a ranked list, allowing them to tie as many candidates they want on any part of the list, allowing them not to rank them, and allowing them to select a list of candidates that they disapprove of absolutely above everyone else, and use this list to vote strategically for them?

Well, here's how the method works:

Every voter votes for their fist choice(s), and then every voter who's first choice is currently losing then also votes for their second preferences.  If there is a new winner then, but a candidate can then become the winner by withdrawing the votes of the voters who voted the current winner second place but him first place, but without causing both of them to lose, then he will withdraw his votes, and the process is repeated until one candidate cannot win by withdrawing or giving their votes.  If your first and second place choices are then losers, you can then throw in your third place votes and the process is repeated, although the ballot could be simplified by limiting the voters to first and second place choices.  

At the absolute end of these rounds, if your vote currently holds the winner as one of your most dissapproved of candidates, you throw in your approval for every candidate except them.  If a new winner is selected the dissapproval votes of the new winner are thrown.  I could see how this could lead to a circular ambiguity, so if it does, then I guess you could simply not count the disapproval votes.  This disapproval round is not needed.  I only added it because a good voting system must not only take into account how much a candidate is liked, but also how much he is disliked.

This method seems to satisfy the Strong FBC, because your vote will not go to the second choice unless your candidate has absolutely no chance of winning.  So you have no reason to rank a candidate the same as your favorite unless they are tied in your mind.  It is also monotonic because, unlike true IRV, it doesn't rely on the elimination of candidates to work.  It also passes the participation criterion, because it doesn't rely on some magic 50% cutoff for the second choice votes to go in, it only gives the second choice votes in once your candidate is surely losing.  I'm not sure whether or not it satisfies the Condercet criterion... it seems to, but I haven't done too terribly much math on it.  I think it really seems to depend on how much information the voter gives out.  It would be an absolutely great thing if it did, though, because it would then be a burying-proof Condercet method, which would be the holy grail of those kinds of voting systems.  It would satisfy the majority
 criterion if you didn't allow people to rank as many people 1st place as they wanted, but I really don't see how limiting voter choice is going to improve the method too much.  From what I can tell from it, it ALMOST satisfies Arrow's Impossibility theorom, except that it is not fully deterministic because it makes a lot of assumptions about voter strategy.  I don't think that's really much of a flaw, though.

Either this is a very darn good, almost perfect voting system or I am doing some extra-ordanirly bad math, which I hope I'm not, because I've made some pretty bold claims and it would be somewhat embarrassing.

I'll try to provide an example of this system to those baffled by my description:

The candidates are D, R, S, L, M  (Democrat, Republican, Socialist, Libertarian, and Moderate, to add some real world logic to the factions)

110 voters: 1st place: D ; 2nd place: M, S ; 3rd place: L 
100 voters: 1st place: R ; 2nd place: M, L ; Disapproved: D, S
50 voters: 1st place: L; 2nd place: R ; 3rd place: M,  D   Disapproved:  S
75 voters: 1st place: M ; 2nd place: D, R ; 3rd place: L
45 voters: 1st place: S ; 2nd place: D ; 3rd place: M Disapproved: L, R

The total first place votes add up like this:

D: 110 votes
S: 45 votes
L: 50 votes
M: 75 votes
R: 100 votes

The current winner is the Democrat, so everyone who's not winning throws in their second place votes:

D: 230
S: 45
L: 150
M: 285
R: 175

Now the Moderate is the winner, and no one can now win by withdrawing their votes from him.  Since the Democrat is now a loser, they would throw in their Socialist and moderate votes, but that won't affect the election so I'm not going to draw a new chart from it.  Since no one disapproved of the moderate no dissapproval votes are cast.

The moderate is the winner.  This would also be the winner in approval and Condercet, so this may not be a wonderful example.  I haven't tested it on an example of a Condercet election that produces a circular ambiguity yet.

So, this method will USUALLY produce the approval winner, but it completely eliminates any reason to vote tactically in approval, so it is a greater improvement than it may seem.  I'm not sure if this completely satisfies non-manipulability, but it seems to, being that it works by manipulating approval to the maximum extent.

What do you think?

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