[EM] Ranked Preferences, example calculations

[Abd ul-Rahman Lomax]

At 02:00 AM 10/27/2006, Juho wrote:
>Ok. I agree that B has the best social utility from "Range
>perspective".

I don't think that way. B has the best social utility from my 
understanding of how society works. If this is a group of friends 
trying to buy pizza, and A and B are pizza flavors, and only one can 
be chosen, B is *clearly* the best choice. Why would elections be any 
different?

That is, healthy group decision process follows certain general 
principles. The Majority Criterion neglects an important part of this.

It does this because of some fuzzy idea that the majority should 
rule. But if I were King, I would not want my whim to override the 
clearly felt needs of my subjects. The issue is not majority rule, 
but *how* the majority rules. A majority can easily control the 
outcome of either style of election (Condorcet, which is pure 
preference, and Range, which is an integrated method, directly using 
outcome-satisfaction estimate but which also can be used preference-style).

That is, if the majority does not want to please the minority, it 
does not care if they are devastated by the outcome of the election, 
if their attitude is "they should get over it," then they can easily 
get what they want. Just vote it as a strong preference. But they 
should remember what happened to the one who said "Let them eat cake."

She lost her head. As did many others.

Systems which do not maximize and spread satisfaction lead to 
revolutions or civil war. Sometimes this can be put off for a long 
time, but we should remember that *the system we have now led to the 
U.S. Civil War,* a devastating conflict. We tend to remember the goal 
of the civil war as being the freeing of slaves, but it is pretty 
well established that this was not the prime issue, it was North 
domination of the South, and slavery was merely one example of this.

Lysander Spooner is one of my heros; he was a fervent abolitionist, 
but he was also strongly -- and consistently -- opposed to the Civil 
War, because he saw, correctly as it turned out, that no good would 
come of coercing the South by force of arms, considered that 
non-coercive methods would be far more effective. And, indeed, in 
most of the world that is how slavery ended. In the U.S., it was a 
tactic of war, intended to damage the South. It left most of the 
former slaves in desperate conditions, with them ending up with no 
real civil rights in much of the country, and it took a century 
before this really shifted.

>  But I'm trying to balance between different criteria
>here.

You are trying to balance between a broken criterion and an effective 
one. The result can only be a reduction of effectiveness.

(Technically, the Majority Criterion is not "broken." It is simply a 
criterion, not a standard. But we have thought of it as a standard 
for so long that I think it is time we explicitly point out how it is 
defective if considered a standard. Majority preference is *often* 
not the best choice. With pizza or Presidents.

Yes, often the two coincide. It is when they don't that the mischief is made.

And thus, respecting the majority principle, I've suggested that the 
election of a Range winner over a Preference winner should be 
ratified by the electorate, either by a pure ratification vote or by a runoff.

A ratification vote is an opportunity to determine, as a single 
question, whether the electorate would prefer to accept, in this 
case, the Range winner, or would not, in which case the election 
would be held anew. If the majority rejected the Range winner, that 
person would be disqualified from running in the new election. This 
candidate has been explicitly rejected by a majority.

If a runoff is held, it would be between the Range winner and the 
Preference winner. It is quite true that if the majority holds to its 
original preference it can prevail. The only problem with the runoff 
is that it practically invites the electorate to do that. However, it 
is the prerogative of the public to make stupid decisions. Further, 
someone can improperly win under Range if the rules are not 
optimized. This is much more unlikely to happen if blanks are counted 
as zero, which is one reason why I've argued for that. But the other 
consideration is that counting blanks as zero makes it almost 
impossible for a write-in candidate to win. I don't think we have 
really worked all this out, which is why the runoff.

Much of the time, maybe most of the time, the Range winner and the 
Preference winner at the same. But it is when they are not that 
something deeper is needed. I don't think it is possible to 
incorporate that something in a single election. What is needed is 
deeper deliberation, which is why another vote is needed.

This is why top-two runoff may be much better than IRV....

>  One strict rule for me when designing this method was to keep
>sincere voting possible and probable. If that would not have been the
>goal I could have picked e.g. Range (that has good utility with
>sincere votes, but that unfortunately can not maintain the sincerity
>in contentious elections).

This is simply a guess, and is probably a bad one. Insincere voting 
damages the utility of the election *for those who vote insincerely.* 
They risk achieving a poor outcome. Essentially, they are taking an 
intelligent process and attempting to confuse it with lies. If a 
majority of people -- or even a strong minority -- are doing that, 
*election methods aren't going to solve the problem.* Except maybe 
for Asset Voting or Delegable Proxy....

Which are not really election methods, since they do not involve 
opposition and losers and winners, if used for multiwinner PR.

That election methods in general leave many voters having cast wasted 
votes, they might as well have stayed home, it would not have 
affected the outcome, is a major problem. The wasted vote problem is 
one of the biggest, and election methods people have mostly wasted it.

>Ranked Preferences tries to find one optimal spot in the space of
>election methods. Let's see if it can be proven to fail or if it can
>be improved.

How long do we have to try? The *major* problem with present election 
methods is, I'd judge, the complete neglect of preference strength. 
There is an additional problem that some methods don't even select 
the Condorcet winner, i.e., the Preference winner. It is completely 
clear that solving the latter problem won't solve the former, but 
solving the former problem *includes* respecting the latter. That is, 
where preference strengths are equal, the Majority Criterion applies.

But the Condorcet Criterion, satisfaction of which requires that the 
pairwise preference winner always win the election, is even worse, 
for it uses a fully ranked ballot. Necessarily, in elections with 
more than two serious contenders, the Condorcet matrix may be using 
weaker preferences than are involved in the Majority Criterion.

I had written in the past that the Condorcet Criterion "is the gold 
standard of election methods." If all we have is preference data, 
that is still true. But the problem is precisely that ranked methods, 
as distinct from range methods, don't collect strength of preference 
data, and if a method uses preference data in the determination of 
the winner, it necessarily does not satisfy the Condorcet and 
Majority criteria.

A>>B>C

is quite a different vote, with respect to B, than

A>B>>C.

But a ranked ballot does not collect this information, it only could show

A>B>C.

A ballot method was proposed that would simply allow the use of empty 
ranks to indicate preference strength.

The most straightforward way to count this is as Range! What this 
idea does is to set up a set of fixed ranks, and the voter assigns 
the candidates to these ranks. This is quite what Range does. 0-99 
Range sets up 100 fixed ranks, and the voter assigns candidates to 
those ranks. Equal ranking is allowed, which most Condorcet proposals 
also allow.

(This is equivalent, in Condorcet, to using Approval Voting in the 
pairwise elections. If someone votes for both candidates in a pair, 
then the ultimate effect is as if the voter had abstained from that 
election. Standard Approval stuff.)

It is not clear that there is *any* "strategy" problem with Range. We 
won't know for sure until we have more data about how Range actually 
behaves in public election. So trying to fix a problem that may well 
not exist, by compromising in a direction that is known to be a 
problem, is a variation on fixing what is not broken. I.e., it 
usually makes things worse.