[Election-Methods] Using range ballots as an extension of ranked ballot voting

[Abd ul-Rahman Lomax]

At 03:20 PM 3/2/2008, mrouse1 at mrouse.com wrote:

>I'm curious about voting methods that take ranked ballot methods and 
>adapt them to range ballots. For example, with Baldwin's method, you 
>take drop the candidate with the lowest Borda score, recalculate, 
>and so on. A range variant might drop the candidate with the lowest 
>range score, normalize the remaining scores, and repeat. It should 
>still give the Condorcet winner (if any) but it might fit different 
>election criteria than standard Baldwin. Likewise, a range 
>generalization of the Kemeny-Young order might be interesting.

There is a fundamental problem with ranked methods, which is that 
ranking neglects preference strength. You can take a Range ballot and 
analyze it as a ranked ballot, and derive some useful information, 
but the reverse is problematic. Borda runs into problems because of 
the assumption of equal preference gaps. Borda *is* a kind of Range, 
but with that assumtion, which is, quite simply, not reflective of 
the real world. Range works, at least in theory, because preference 
strength *is* important, particularly to the only reasonable method 
of election performance that I'm aware of, social utility (making the 
assumption that the full range of satisfaction of each voter is as 
worthwhile as the full range of satisfaction of every other voter; 
the common objection about non-interpersonal-comparability of 
utilities is based on ignoring this assumption, which is pretty much 
fundamental to democracy.)

I've proposed that, in fact, Range ballots be analyzed as ranked 
ballots, pairwise. I've never fully specified a method, but the basic 
idea is that if the Range winner is beaten by another candidate, 
pairwise, there is an actual runoff election.

One of the realizations I've come across in the last year is that 
runoff elections test preference strength, that the claim that 
runoffs are unfair is probably incorrect. Real top-two runoffs seem 
to reverse the vote in about one-third of the cases, from my 
examination of a limited number of such elections; but IRV, so far, 
isn't generating that reversal, and there is very strong preservation 
of preference order in each IRV round. The plurality winner is the 
final winner, and the runner up is still the runner up, and it goes 
deeper than that in some of these many-candidate elections in San Francisco.

Replacing Top-two runoff with IRV is practically insane. With very 
few exceptions, the IRV winner still did not get a majority of the 
votes cast in the election, and it is only by discarding exhausted 
ballots -- that contained valid votes -- that an apparent majority 
appears. This is entirely contrary to the principle of requiring a 
majority in the first place, which is why top-two was being used to 
start with. Given that IRV seems to be almost always choosing the 
plurality winner, why not stick with Plurality? Or a method more 
likely to find a true majority. (IRV is sometimes declaring a winner 
who *does* have a majority, but it's concealed underneath other 
active preferences.)

Some of the San Francisco IRV elections generated enough data to do 
Bucklin analysis, and Bucklin did find a majority more often, from 
the same votes. Same results, of course. But a heck of a lot cheaper 
to count.... And it was used for a long time in the U.S., and was 
apparently popular.

Anyway, Range with runoff as I described would be uncontestably 
Majority Criterion compatible. It can detect Range failure due to 
voter misapprehension of the true situation, correcting for strategic 
voting. I think it's a really interesting idea.... Smith's 
simulations found Range with runoff to be better at S.U. maximization 
than pure range, probably due to normalization error. That was simply 
top-two runoff Range, no pairwise analysis was performed, but almost 
always, if there is a pairwise winner over the Range winner, that 
candidate would, in fact, be the Range runner-up.

Another modification of Range is to explicitly define an approval 
cutoff, and require a runoff if the winner isn't approved by a 
majority. Same with Approval voting, actually. Should require a 
majority to win (and a double majority, the situation where Approval 
allegedly fails the majority criterion, is not a majority choice, and 
a runoff fixes the problem.