[EM] 3 or more choices - Condorcet

[Juho Laatu]

On 30.9.2012, at 15.41, Kristofer Munsterhjelm wrote:

> On 09/30/2012 12:51 AM, robert bristow-johnson wrote:

>> i still think that a cycle with a Smith set bigger than
>> 3 is soooo unlikely since i still believe that cycles themselves will be
>> rare in practice.

...

> Currently, single-winner elections very rarely have cycles and large Smith sets are even more rare.

In typical political environments where people know the candidates or at least the parties well, and where there often are also strong established orders like teh left-right axis, cycles are indeed quite rare, and cycles bigger than 3 are even more rare.

There can be however environments where cycles are somewhat more common. I mean environments where all the candidates look quite similar, there are many of them, and where there is no strong eastablished political structure that would help voters in making decisions. In such an environment there could be "random loops" among the very similar candidates. For example in the 2008 Wikimedia borad elections there was a large loop, but not at the top (http://meta.wikimedia.org/wiki/Board_elections/2008/Results/en).

But in typical political elections top cycles of 4 should be very rare.

> As far as intrinsically Condorcet methods go, Ranked Pairs feels simple to me. The only tricky part is the indirect nature of the "unless it contradicts what you already affirmed" step.

To me the biggest problem of path based methods is that there is no very good real life explanation to why chains of pairwise victories are so important. In real life the idea of not electiong a candidate that would lose to someone who would lose to someone etc. doesn't sound like an important criterion (since it doesn't talk about what the candidate is like or how strong the opposition would be, but about what the set of candidates and its network of relations looks like). Probably there will never be a long chain of changes from one winner to another in real life.

Juho


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