[EM] Range Voting in presence of partial information of a certain character

[Abd ul-Rahman Lomax]

At 09:13 PM 5/20/2010, fsimmons at pcc.edu wrote:
>Thanks for the comments Kevin and Lomax.
>
>Let me start over in the same vein:
>
>Suppose that candidate X was just announced as the winning candidate, and no
>indication was given of how the other candidates fared in the range 
>style election.
>
>How would you wish that you had voted your range ballot?

Weird circumstance, eh? I don't know how close it was?

>Personally, I would be mostly satisfied with my ballot if I had given max
>support to everybody that I preferred over X, and no support for 
>anybody I liked
>less than X.

Sure, the same. But that's not the only ballot I'd feel satisfied 
with. In particular, if I had a favorite, not just some candidate who 
I thought was totally irrelevant, and I rated someone else the same 
as that candidate, I'd not be happy. Because I didn't express my 
preference, even though it was, in the end, irrelevant. If it's going 
to be that the other results are never announced -- what kind of 
system is this? -- then that expression is completely moot. It's not 
moot in real elections, unless there is massive fraud.

>But what about X ?  I could say that since X was the winner, X probably didn't
>need my support, so I would wish that I had not supported X at all.  But if
>everybody took this attitude, then everybody would regret their support for X,
>except those that preferred X over all of the other candidates.  And 
>most likely
>X could not have won with support only from those who considered X 
>as favorite.

That is contrary to your initial condition, probably.

>Suppose that due to some technicality the election had to be repeated.  Would
>you give any support to X this time around (still not knowing 
>anything about how
>the other candidates fared) ?

Well, I'm proposing Range ballots feeding Bucklin "instant runoff 
approval." So I'd know from this far more about the preferences of 
others, and I could make my choices over a real understanding of 
probabilities. I'd already know if and what other candidates had some chance.

But, given the highly artificial constriction, I know nothing more 
than I knew in the first place. Forest, you set the condition that X 
was very likely to win. That's all you know for the second ballot, 
why should your decision be different?


>In my last message under this topic I suggested that perhaps the 
>thing to do in
>the case of a sure or almost sure winner (when you know nothing about the
>chances of the other candidates) is to just give them your sincere rating.

Yeah, that part is correct, I believe. However, if you know the 
identity of the frontrunners, you can make a better choice. But not 
much better!

The only place where there is a problem with "sincere voting" is when 
the "sincere ratings" are distorted by the presence of irrelevant 
candidates about whom you have strong feelings (for or against).

>Sincere ratings can be constructed by asking questions like this:  Would I
>prefer X to a lottery of 31%favorite+69%worst?  Suppose that the 
>answer is yes,
>but when the same question is put with the percentages changed to 29 
>and 71, my
>answer changes to no.  Then my natural rating for X would be about 30 percent.
>
>What is the point of all of this?   I'm looking for a DSV (Declared Strategy
>Voting) method that takes sincere natural ratings and converts them into
>strategic range ballots in such a way that when the winner is announced, the
>voters will be as satisfied as possible with the way the DSV handled 
>their ballots.

Bucklin. It's been done, to a degree. The ballot becomes clearer in 
meaning if the election requires majority approval; this ties 
approval to voter preference for a resolution in the first ballot vs 
the risk and inconvenience of a runoff. So "approval" means "I 
approve this candidate in preference to holding a runoff election 
under the rules."

If most voters prefer to see a runoff, it certainly seems fair to me 
to hold one!

For practical voting methods, for public use, I believe that it is 
necessary that the method of using the votes be very clear and 
simple. I'd allow a little more complexity, but not much more, in 
determining who is in a runoff election if one is to be held. 
Eventually, with a lot of ballot experience, it might be possible to 
eliminate more of the runoffs, but it would start, I'd suggest, with 
a runoff whenever no majority is found. Because some elections with 
majority failure make it obvious who would have won, among the 
possible choices, in an "instant runoff," because the margin is so 
close and nobody else is in range of winning, it does seem prudent to 
allow some elections to complete short of a majority. With good 
ballot data, it's possible to measure the regret involved and to make 
this decision in a far more accurate way than simply requiring a 
fixed percentage. The use of 40% in Burlington is *awful*....

Bucklin was used, was very popular, is easy to count, and makes the 
most sense as a primary method in a runoff environment, seeking a 
majority. It was never used for that; like IRV, it was sold as a 
runoff replacement. Bad Idea. Sometimes the electorate doesn't have 
enough information to make up its mind!

Bucklin is like a declared strategy method, if I understand the idea, 
where one has a bot voting for you in a series of approval elections, 
where the bot adds in additional approvals according to the "round 
number," using your ratings of the candidates to decide when to vote 
for you for any given candidate, if ever. The ranks on an original 
Bucklin ballot are the approved ratings from a Range 4 ballot, and 
they had the original restriction that overvoting in the top two 
ranks was prohibited, I'd dump that, there is simply no justification 
for it. (Bucklin gives so much freedom to express the Favorite that 
it's silly to worry about multiple majorities in the first rank and 
therefore possible Majority criterion failure. In reality, majority 
failure seems to be, long-term more likely, though Bucklin was, in 
municipal elections of high interest, very good at finding 
majorities. Only people who have no significant preference will vote 
for more than one candidate in first rank.)

Original Bucklin allowed skipping ranks, your vote in each rank was 
independent, except that you were not allowed to vote for more than 
one rank for a candidate (they counted it as the higher expressed 
rank, and they counted overvotes in an exclusive rank as no vote in 
that rank, I think. I'm not sure about the exact details, and they 
may have varied with jurisdiction.)

To my knowledge, this analysis of Bucklin as a sincere Range ballot, 
confined to the approved ratings, is original, but perhaps someone 
else has noticed it before me. It doesn't seem that obscure....

And then that holy grail, in a runoff system, becomes possible: a 
system which satisfies not just the Majority Criterion, but the 
Condorcet criterion as well, that seeks maximum approval, and that 
will allow a Range winner to defeat a Condorcet winner -- but only in 
a runoff, where the electorate explicitly makes that choice. To fully 
do this requires doing three kinds of analysis on the Range ballots 
feeding a Bucklin system, the most difficult being Condorcet 
analysis. It's not necessary if there is a single-candidate majority 
in the first rank, for sure. And it need not be full Condorcet 
analysis, it merely need be a pairwise comparison with whomever might 
otherwise win the election.

It's not hard to understand at all. But I'd rather see more interest 
before starting to develop very specific proposed rules.