[EM] Partial preference sets and intransitive preferences

[MIKE OSSIPOFF]

Dear Jobst--

Sure, ideally the voter should have the options that you spoke of: Voting 
preferences between certain pairs of candidates, without having to vote 
preferences between other pairs among those candidates. In your example, 
voting A over B and C over D, without having to vote between any other 
pairs.

If that voter, with a ranking, wanted to not vote between A & C, s/he'd have 
to vote C equal to A, and over B, for instance. Ideally s/he shouldn't have 
to vote more preferences than s/he wants to.

You pointed out how it could happen that a voter could have good reason to 
vote an intransitive set of pairwise preferences.

I'm in favor of letting the voter vote only those pairwise preferences that 
s/he wants to, and vote intransitive sets of preferences if s/he wants to. 
The reason why I don't propose it for public elections is because of course 
it complicates the voter's choices and the balloting procedure. A ranking is 
simpler. But simplicity is the only advantage of a ranking over the more 
general preference expression that you suggest.

For future EM polls, how about letting a ranking be an _option_, while also 
allowing the option of separately-written pairwise pairwise preferences, as 
many or as few as the voter wants to vote, and which needn't be transitive.

But it would have to be made quite clear that that more general 
preference-voting is only an option, and that the voter can also vote the 
simpler ranking if s/he wants to.

Likewise for some organizations of people who would like somethig more 
expressive than rankigs, and would accept it as a balloting option, along 
with the ranking option.

But for public elections, it seems to me that the more general 
preference-voting would intimidate or confuse voters. Even offering it as an 
option would make people think that they don't understand the balloting, and 
would make them tend to reject the electoral reform proposal, or decline to 
vote. But I also wouldn't include AERLO, ATLO, etc. in an initial public 
Condorcet proposal either. For the first Condorcet proposal, start out with 
un-enhanced Condorcet. Then the enhancements can be proposed at a later 
date.

Again, though, there's no reason to not allow those options in EM polling, 
and it would be interesting.

Mike Ossipoff




You wrote:

Now, this is again a situation where I don't understand why everyone on
the list always just talks about quite a special type of preference
relations, namely rankings. Why don't they finally realize that rankings
do not satisfy the above requirement? This is even harder to understand
when examples of such preferences are so easy to construct: Prefering A
to B and C to D doesn't imply at all prefering either A to D or C to B.
But when I express A>B and C>D in ranking, I must also express either
A>D or C>B also. These preferences just don't fit into any ranking.
Instead, they build a *partial* ordering whose diagram looks like this:

	A   C
	|   |
	B   D

There is even enough evidence that people sometimes have *cyclic*
preferences when applying more than one criterion for comparing the
options. And I definitely think that those people should be allowed to
express these preferences, too. Example: Anna should be allowed to
express A>B, B>C, and C>A, meaning that when the final choice is between
A and B she would like to have A, when it's between B and C she would
like to have B, and when it's between C and A she would like to have A.

Most of our favourite election methods can easily cope with general
preference relations instead of just rankings when reformulated in the
right way! So why don't we finally stop talking on rankings and start
talking about pairwise preferences?

Sincerely, Jobst

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