Methodology: Favorite-Burial, Condorcet’s Criterion, ICT and Old Condorcet

by Michael Ossipoff

July 27, 2012

In this next article for Democracy Chronicles, I would like to discuss the voting methodology Improved Condorcet Top (ICT) in regard to a precise definition of one of its desirable properties.  I will include an answer to a recent claim about an advantage of ordinary Condorcet and a comparison of ICT to ordinary Condorcet.

Condorcet’s method is one of the most popular classes of voting systems along with Approval. Condorcet, broadly defined, in some form or other, has long been popular with voting system reform advocates and people who are invested in voting system discussions. I introduced and advocated the winning-votes variety of Condorcet, because it has strategy properties and guarantees above average Condorcet versions.

More recently, I have been advocating Improved Condorcet, devised by Kevin Venzke. I propose the Improved-Condorcet-Top version of it, devised by Chris Benham because of its superior properties.Before I continue, I should clarify that, though I consider ICT the best method for polling, I recommend only Approval as a proposal for public political elections, mainly because Approval is a lot easier to propose and enact than any rank method. I provide an explanation as to why this is, in my Approval article.

It’s not to say that I don’t think ICT would be good for public elections; it would be great, because, in addition to Approval’s freedom from the need to vote someone over your favorite, ICT brings defection-resistance, as described in a recent article of mine published on Democracy Chronicles.

To clarify, ICT would be great if the electorate would agree when ICT’s favorite-burial guarantee is described.In this case of the elegantly simple Approval that guarantee is obvious. If you approve Compromise and not the worst, then you’re fully helping Compromise against the worst, even if you also approve Favorite. Though ICT also has that guarantee regarding top-ranking, it isn’t as obvious, and there’s always the possibility that the guarantee wouldn’t be believed and that some voters would still favorite-bury.

Thus, the reason that I recommend Approval instead of ICT for public proposals is mainly because Approval is more executable than rank methods; but, also because Approval’s favorite-burial guarantee is more obvious. Another reason is Approval’s simpler and less costly implementation.

I consider the Improved Condorcet versions to be Condorcet versions.  They differ from the ordinary Condorcet versions in how the verb ”beat” is defined, in regards to how they interpret equal-top-ranking.  So let’s compare ICT to the more usual Condorcet versions, which I call “ordinary Condorcet”. First, a little table-of-contents for this article’s topics:

1. A precise definition of a criterion to measure a method’s freedom from need for favorite-burial strategy.

2. An advantage that some claim for ordinary Condorcet.

3. Comparison of Improved Condorcet with ordinary Condorcet.

I won’t go into the subject of ICT’s defection-resistance here, its avoidance of the “chicken-dilemma”, the co-operation/defection problem, or the “you help, you lose” problem, because I covered that topic in another recent article, an article about the new ICT poll. Now, to discuss the topics listed above.

First, a precise definition of a criterion to measure a method’s freedom from need for favorite-burial:I call it the “Favorite-Betrayal Criterion” (FBC). One could also regard that as standing for “Favorite-Burial Criterion”. In voting system discussion, the term ”burial” refers to insincerely ranking a candidate below someone you like less.  The definitions:FBC1 Premise:V is a set of voters who all have the same preferences and vote in the same way. Everyone other than V has already voted.Requirement:

By voting someone over their favorite, V shouldn’t be able to gain an outcome that they prefer to every outcome that they could get without voting someone over their favorite.

FBC2 Premise:

Same as FBC1, plus this: The only way that V can keep Worst from winning is by making Compromise win instead. They have a way of voting that can achieve that.

Requirement:

If V votes everyone over Worst, and doesn’t vote anyone over Compromise, then Worst won’t win.

FBC3 Premise:

Same as FBC1, plus this: Set A and Set B are disjoint sets of candidates. The winner will come from Set A or Set B. V has a way of
voting that would keep the winner from coming from set B.

Requirement:

If V votes everyone not in set B over the Set B candidates, and doesn’t vote anyone over any of the Set A candidates, then the winner won’t come from Set B. FBC1 was the first FBC version. It’s often referred to as Weak FBC. I suggest, for it, the names of “FBC1″ and “Weak FBC”.  When I say “FBC”, without a number, I’ll be referring to FBC2. FBC2 and FBC3 might be equivalent to each other.  Approval and iCT pass all three of the above-defined criteria.  Ordinary Condorcet fails all three of the above-defined criteria.  To discuss a claimed

advantage of ordinary Condorcet, first, let me define ordinary Condorcet:

X beats Y if the number of voters ranking X over Y is greater than the number of voters ranking Y over X. Any candidates who are not beaten are winners and typically there is only one such winner. If there are no winners, then various versions have various ways of choosing a winner. Those are called “Condorcet completions”. We needn’t go into them.  Here’s the popular criterion met by ordinary Condorcet:

Requirement # 1: The method’s balloting must allow the voter to vote as many candidates as he or she wishes over each other in any transitive order that he or she wishes.

Requirement #2: If a candidate beats each of the others (as defined above), then he or she must win.

Now, critics of ICT object that ITC doesn’t meet Condorcet’s Criterion (CC), and that, in fact, FBC and CC are incompatible. Now I’d like to respond to those claims: ICT’s violation of CC isn’t a meaningful violation. If someone claims that it is, I would ask that person whose rights are violated in that criterion violation.  Suppose that you rank X and Y both, together, in 1st place. In ordinary Condorcet, ranking Y in 1st place can let it beat X, and thereby cause X to lose, resulting in a win for someone you’ve ranked below X and Y. Likewise, ranking X in 1st place can let it beat Y, and thereby cause Y to lose resulting in a win for someone you’ve ranked below X and Y. Now, I ask: Is that what you want, when you rank X and Y in 1st place?

You rank X and Y in 1st place because you’d prefer that one of them win.  Therefore, what ordinary Condorcet can do, as described above, is contrary to your wishes, when ranking X and Y both in 1st place. Because you want X or Y to win, you’d want to use your voting power to prevent one from beating the other.You’re doing that in Improved Condorcet.  That’s why Improved Condorcet is called as such; it’s an undeniable improvement over ordinary Condorcet.

As I said, when you rank X and Y both at top, you do so because you want one of them to win. That’s why Improved Condorcet counts an equal-top ranking of X and Y as a vote against either beating the other. That’s what you’d want, if you want the winner to be one of those two. Improved Condorcet complies with the voter’s wishes better than ordinary Condorcet does.

Do Improved Condorcet methods, such as ICT, fail Condorcet’s criterion? Not if “beat” is defined consistent with the voter’s wishes when he or she ranks X and Y both in 1st place. Not if that equal-top-ranking is interpreted consistently with what the voter wants when they rank X and Y both in 1st place. With that definition and ranking-interpretation made consistent with the wishes of the equal-top-ranking voter, ICT meets CC, and CC is not incompatible with FBC.

Articles by Michael Ossipoff on Democracy Chronicles:

Democracy Chronicles interview with Michael Ossipoff: