[EM] A four bit (sixteen slot) range style ballot

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 11:53 AM 6/11/2010, Kevin Venzke wrote:

>> But you say this and then quote Woodall's Majority criterion, which
>> Plurality fails?
> 
> Plurality allows voters to place a candidate at the "top of their 
> preference listings." Does Plurality fail Woodall's Majority Criterion? 
> That depends on interpretations. The criterion was not designed and 
> defined well enough to be sure. What is a "preference listing"?
> 
> There is social choice theory and there is election method theory and 
> they are not actually the same, though they are certainly related.

Woodall's Majority criterion is what is called "mutual majority" on this 
list. It means that if a majority of the voters rank a certain set ahead 
of all others (but with different ranking within that set), then the 
winner must come from that set.

Plurality fails that criterion. Bucklin and most of the advanced 
Condorcet methods pass it. Approval (and all methods that pass ordinary 
Majority) "passes" it if you restrict all ballots to being two-slot, but 
if not, it doesn't.

>> > > * Majority. If more than half the voters put the same
>> > set of
>> > > candidates (not necessarily in the same order) at the
>> > top of their
>> > > preference listings, then at least one of those
>> > candidates should be elected.
>> >
>> > The way this criterion is worded, Approval satisfies the
>> > criterion based on actual votes, but not necessarily based
>> > on internal preferences, for that majority might, for
>> > example, all prefer A to B but actually vote for A and B.
>>
>> But within Woodall's framework, all methods have to be interpreted as
>> rank. Woodall uses an interpretation of Approval so that it will fit in
>> his framework. You don't have to use that interpretation. But arguing
>> about whether a method satisfies a Woodall criterion without any attempt
>> to stay within Woodall's framework seems futile.
> 
> Basically, the term "Majority Criterion" went on to be used by others in 
> various ways, with various definitions and interpretations.

Consider the wording "(not necessarily in the same order)". If he only 
meant equal-rank, then that would be pointless because you can only 
equal-rank in one order. What he means is that if a majority put the 
same *set* of candidates at the top (above all others) of their 
preference lists (orderings), then someone from the set ("at least one 
of those candidates") should be elected.

If you still think this is just ordinary majority, check 
http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM , where Woodall explicitly 
says that Majority is the two-seat version of the Droop proportionality 
criterion, which involves sets. Quoting Woodall:

"DPC. If, for some whole numbers k and m satisfying 0 < k <= m, more 
than k Droop quotas of voters put the same m candidates (not necessarily 
in the same order) as the top m candidates in their preference listings, 
then at least k of those m candidates should be elected. (In the event 
of a tie, this should be interpreted as saying that every outcome that 
is chosen with non-zero probability should include at least k of these m 
candidates."

Here, he states outright "as the top m candidates in their preference 
listings".

>  From there I realized that the ballot could be full Range and that 
> therefore, from it, a Condorcet winner could be detected, and if this 
> winner differs from the Bucklin/Approval/Range winner, a runoff could be 
> triggered. What this amounts to is the rough equivalent of a 
> ratification combined with a runoff. Range voting easily may fail to 
> satisfy the basic democratic principle of majority rule, so, 
> technically, a Range result should be ratified. To be efficient, though, 
> the ratification may be combined with a consideration of at least one 
> alternative, and perhaps two or three. With a good voting system, and 
> with what have become, in the runoff, well-informed voters, having the 
> results of the first poll -- which could be printed on the ballot! -- 
> majority ratification of a result is quite likely.

Isn't that just letting the people strategize? It seems to me that 
different people would have a different capacity to actually do so, in 
which case we should let the method itself do the strategizing (through 
some form of DSV) instead of having to provide every voter with poll data.

There could still be runoff afterwards, of course.