[EM] IRV vs Plurality

[Abd ul-Rahman Lomax]

At 03:04 AM 1/26/2010, Juho wrote:
>On Jan 26, 2010, at 4:43 AM, Abd ul-Rahman Lomax wrote:
>
>>At 07:22 PM 1/25/2010, Juho wrote:
>>
>>>There are many (working) uses for an approval cutoff in ranked
>>>ballots. But on the other hand they may add complexity and confusion
>>>and not add anything essential. => Careful consideration needed.
>>
>>Only a voting systems theorist who is not a parliamentarian or
>>familiar with the principles of parliamentary traditions, essential
>>in direct democracy, would think approval not relevant. Approval is
>>Yes/No on the series of possible choices. It's fundamental,
>>actually, and compromises with this are *never* made in direct
>>democracies, they are only made in the name of efficiency in large- 
>>scale elections.
>
>I referred only to approval cutoffs as additional components in
>existing methods.

My point is that "approval" is a separate issue from ranking, and 
it's actually a crucial issue in multiple-choice decision-making in 
general. I've seen, after an approval poll in a context where the 
first preference of most members was about 70% for one option, but an 
approval polls showed little more than that as approval for that 
option, but 99% approval for an alternative, a motion to adopt the 
alternative, seconded and passed with no dissent at all, unanimity. 
The only way to discover a situation like this is some later poll, 
repeated election. Had the original poll been an actual election, 
choosing the highest approval would have, in fact, implemented the 
will of the majority. Usually. That's why approval voting is 
reasonable, but also why runoff elections or similar tests are 
sometimes needed. Note that, in a situation where they already knew 
(this was show-of-hands voting, and the status quo voting was first) 
that they had a strong majority, the 70% nevertheless approved also 
the alternative, probably based on the thorough discussion that had 
preceded the poll. They understood the depth of feeling behind the 
opposition to the status quo, and, seeking the common welfare, which 
depends on organizational unity, they allowed the other option to 
prevail by approving it as well.

In repeated polling, approval is an excellent way to rapidly seek a 
majority; in contentious issues without adequate deliberation, such 
polls may start out as largely bullet-voted, but as the process 
continues, approvals will be added, and some prior approvals might be 
dropped (representing an actual change in preference order, a 
phenomenon possible in repeated elections and obviously impossible 
with a single-ballot. In the situation I described, many of those 
preferring the status quo -- which had stood for maybe forty years -- 
had said, at first, "over my dead body." I'd call that strong 
disapproval, eh? But, after discussion and expression of many 
different member sentiments, those members obviously changed their minds.)

>>Yes. However, "designed to elect candidates with no core support" is
>>an overstatement. It certainly is not designed for that, but it
>>allows it. It's pretty unlikely, eh?
>
>Yes, but desirable if one wants to respect the basic philosophy of sum
>of ratings.

Right. Setting aside the issue of using averages, which I consider 
foolish as a practical proposal at this time, but which, when we get 
real Range elections happening, sum of votes obviously maximizes 
expressed expected satisfaction with the various outcomes. Range 
voting is interesting precisely because it bases outcomes on a metric 
for election performance, and the only issue is a lot of hot air 
about "strategic voting" in Range.

My view on this is simple: strategic voting in Range expresses real 
preference strength. In other words, it's an oxymoron, created by an 
assumption that when a voter "exaggerates," the voter doesn't really 
care that much. But how much we care always depends on our perception 
of realities.

If a range outcome benefits me to the tune of $100, and another costs 
me $100, other things being equal, what's my preference strength 
between these. We can assign an absolute value ($200) to the 
preference strength, but that does not determine a sensible Range 
vote. If those are the only two options, the vote strength I will 
exercise is 100% between them. But say there are two more options, 
but all of them are considered by me to be impossible, the other 
voters won't support them. Suppose with one of these options, I gain 
$1000, and with another, I lose $1000. Does this change my "sincere vote"?

I say no. But with unlimited Range, sure, I'd honestly state the 
actual utilities, as long as the analysis made sense (as with a 
Clarke tax). With normalized range, which is what we ordinarily see, 
I will express, reasonably, my utilities within a truncated set, 
where unrealistic alternatives are excluded. I have called this 
"magnification," because a "sincere vote" represents only the 
spectrum including realistic candidates. Which then indicates, with 
Approval, an obvious and oft-suggested strategy.

This was studied by Dhillon and Mertens in their paper, Rational 
Utilitarianism, and they show that with this voting strategy (more 
precisely stated as voting von Neumann-Morganstern utilities), Range 
Voting (including Approval) satisfies a set of Arrovian criteria that 
are reasonable modifications that allow for the consideration of 
expressed preference strength and equal ranking and, perhaps, I'm not 
sure, a better IIA definition. More than that, it's a unique 
solution. The math is complex and difficult, I'd say, Warren Smith 
claims that the article uses "notation from Hell." But, to my 
knowledge, no errors have been found in the paper.

>There is no good definition of core support. It is quite possible that
>there are elections where core support or weight on first preferences
>is a desirable feature.

It could be argued that whenever "core support" exceeds 50%, this is 
a proper use. With some methods, it's possible to detect that there 
could be a better winner, but a candidate with core support like that 
should never be unconditionally rejected, that's my position. To 
reject the candidate requires a runoff that accomplishes this, explicitly.

>  But it is hard to discuss and judge as long as
>that feature is not well specified (I don't consider the operational
>definition as derived from how IRV works to be a proper definition).

The definition from FairVote is preposterous, in fact, for any 
practical use. It is designed to deflect criticism of IRV, which 
passes the definition, but which substantially fails core support 
with a reasonable definition involving more than zero votes in first 
preference, while maintaining the criticism of other methods, which 
properly give one vote the strength of one vote!

If we are considering a compromise winner that will substantially 
unite the electorate, and that winner turns on one vote in first 
preference, is this any different, in substance, from zero votes in 
first preference? Where does a realistic core support criterion come 
into effect?

And, then, how desirable is core support, actually. If we have a 
seriously polarized electorate, evenly divided between left and 
right, and perhaps even separated as to preference strength (i.e., 
there are no voters in some middle segement), we will see core 
support making this a hotly contested election, and no result is 
really satisfactory; whatever happens, half the electorate will be 
substantially dissatisfied.

But now add to this a centrist. By the terms, there are no voters in 
the middle segment, no voters who will prefer the centrist. (In 
reality, of course, there is the candidate himself and his mother.... 
i.e., it will never be zero in any real election.)

Why, pray tell, is the centrist a poor outcome for the election -- 
and criterion failure implies a poor outcome? It's a result which 
could avoid a civil war or massive civil disobedience. As described, 
the centrist will be the sincere second preference of all the voters. 
Some voters will truncate, being the outliers in each wing, who will 
still have strong preference against the centrist, but others will be 
closer to the middle, and will express the preference.

But in first preference, the centrist is dead in the water, and will 
be rejected in top-two runoff and in IRV, the same. Only in methods 
like Bucklin or Range does the centrist have a chance, and surely 
that's deserved. So Bucklin/Runoff would quite likely result in the 
centrist being in the top two, plus the most popular of the extremist 
frontrunners. If not, here is why: the strong majority of voters 
don't want a compromise, they want a battle between the two sides, 
and when two matched sides both believe they can win a battle, all 
they have to do is try hard enough, expect a battle. If the issues 
involved are the kind people are willing to die for -- and kill for 
-- there will be a lot of dead people.

And when that is the situation, my advice is leave the country, as 
quickly as you can, because it is rapidly getting very dangerous. The 
problem won't be fixed by mere voting systems. If you adhere to one 
of the sides, you won't listen to this advice, and if you don't, 
well, by the definition of the problem, you don't exist, but maybe 
there are a handful who can be saved. Return only when the sides have 
learned that if they don't talk to each other, and actually and 
positively seek reasonable compromises, they will both lose.