[EM] [CES #6990] Re: Wow: new, simple Bucklin motivation for CMJ. So renaming to Graduated MJ.

[Abd ul-Rahman Lomax]

At 09:30 PM 1/8/2013, William Waugh wrote:
>On Tuesday, January 8, 2013 2:04:06 PM UTC-5, Abd ul-Rahman Lomax wrote:
>At 09:34 PM 1/7/2013, William Waugh wrote:
>> >If I were a strategist for a party that has not had a plurality but
>> >may be coming close to one, I would see no reason to treat any kind
>> >of Bucklin election differently from an Approval election, unless I
>> >am missing something.
>>
>>It is an Approval election, just staged. Instant Runoff Approval
>>would be pretty accurate.
>>
>>
>> >For Approval, I'd have to teach my voters to make randomized choices.
>
>Ah, that's not necessary if the method is Bucklin. This is going too
>far. "It's Approval, therefore randomize for an intermediate choice."
>
>
>In the US presidential election, I expect my opponents to bullet 
>vote, and I don't expect them to find a majority if my faction is 
>close to plurality.  It will be a three-way race among factions that 
>are each near 1/3 of the electorate in size.  So the Bucklin grades 
>will collapse together, resulting in an Approval election.  So, we 
>have to use Monte Carlo methods to make the effect that of a Score election.

Real voters don't vote like that! There is an idea here of 
"opponents." There is a "U.S. Presidential election," which is a very 
unusual situation, an indirect election through a bizarre 
misapplication of a old -- great -- idea, that could actually be 
Asset voting if electors were assigned through Asset voting on the 
state level, which *states could do,* constitutionally. (States have 
total freedom and power over how the electors are chosen. The party 
system was *not* anticipated, apparently, by the constitutional 
convention, and it became established because it favored the majority 
party in each state, and for that majority party to go to a fair 
distribution of electors would be politically suicidal if others did 
not go the same way.)

In a three-party system, as described, a voting system is severely 
challenged. But that system is highly artificial and unrealistic. 
Yes, you could realistically have a three-party system were first 
preference is balanced like that.

But parties don't own voters. And individual voters will vote 
differently, depending on their preference strength. Some will bullet 
vote (as assumed, and, in fact, if all voters do that, as expected, 
*there will be no votes in second and third rank.* But some voters 
will add additional preferences, *because their preference for the 
Favorite will be weak.* This can be predicted from any normal 
distribution in issue space.

The assumption here is pure Bucklin, plurality win.

Yes, voters can add randomized choices for an effective intermediate 
vote, but where would this vote be placed? 2nd rank? 3rd rank? If 
second rank, it's silly; instead, one would just use third rank. If 
3rd rank, sure.

However, there is a much better choice: fix the voting system to 
handle this kind of situation better. There is some question of how 
far we should stand on our heads to handle a situation that is highly 
unlikely to arise. What's seen in many-party TTR elections is huge 
vote-splitting, with two parties leading, but still with less than 
30% of the primary vote. There is no doubt but that Bucklin would 
pull up the numbers. Voters could express a clear favorite, providing 
valuable information, while also participating in a *virtual runoff.*

France could use Bucklin for their Presidential primary. There is 
practically no doubt that it would improve election performance, 
given historical data.

So how to improve on Bucklin. I have generally assumed Bucklin, now, 
as a primary method in a maximum two-round runoff system. We know 
that simulations show that runoff range improves performance over 
single-ballot range, given realistic voters.

(If voters voted "accurate sincere utilities" this improvement would 
not happen. If they vote "strategically," which is how people make 
choices, in the real world, the improvement is definite. If they 
simply normalize, normalization error can occur, and normalization is 
probably essential.)

If a Range ballot is used, and if it includes Approval information 
(which is simplest by considering 50% range or above as "approval"), 
we have a fairly simple system for Runoff Range. To win the primary, 
one must have the highest Range vote *and* majority approval. If no 
candidate has majority approval, there is a runoff. This will handily 
address Mr. Waugh's situation, in fact. If they want, they can 
express their preferences in below-approval range, bullet voting for 
the Favorite *as to approval.* Or if their preference is weak, and 
they would rather avoid a runoff if possible, they can add an 
above-approval additional preference.

But more becomes possible. The Condorcet Criterion is the most 
intuitively appealing of voting systems criteria. Because a Range 
ballot allows pairwise comparison, the votes can be tested for a 
Condorcet winner who would *not* appear on the runoff. If one exists, 
then the runoff candidates would shift. It's possible for a runoff, 
with an advanced ballot, to have more than two candidates, but it 
might just be simpler to make the contest in the runoff be between 
the Range winner and the Condorcet winner. (i.e., a little more 
broadly, any candidate who beats the Range winner pairwise. That 
*could* be three, and I'd want to study the situation in detail to 
determine an optimal choice under that circumstance.)

Bucklin starts as descending cumulative approval. Traditionally, it 
terminates once a majority is found. Because of the possibility of 
multiple majorities, how to handle them must be scrutinized. Multiple 
majorities may represent *real approval* of more than one, or could 
represent poor strategic voting choices. Runoffs *test preference 
strength,* and this must be understood to understand the value of 
runoffs. They also produce a difficult-to-quantify value, increased 
scrutiny of a reduced candidate set.

Dark horses *can win* with runoff voting, because the bar is lower. 
In TTR, they only have to make it to second place to get into the 
runoff, and suddently they are not dark horses any more. They are 
frontrunners, and their supporters will turn out in droves in the 
runoff. It becomes a real race! And this is probably why there is a 
"comeback election" in about a third of real nonpartisan runoffs, a 
phenomenon that hardly ever happens in IRV, as a simulation of 
runoff. The plurality leader almost always wins IRV, because the 
voters supporting eliminated candidates appear to be a fair sample of 
the whole electorate *as to preferences among the remaining candidates.*