[EM] IRV vs Plurality

[Juho]

On Jan 26, 2010, at 8:44 PM, Abd ul-Rahman Lomax wrote:

> 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.)

The scenario that you described requires some goodwill among the  
voters. If the competition is really strong then one could expect the  
70% of the voters not to even mention the 99% approved candidate in  
the polls if they already know that they have 70% majority behind  
their first preference.

On the other hand the availability of reliable poll information may  
reduce the competitive spirit of the election. Some part of strategic  
voting and strong competitiveness is based on the fear of unknown and  
lack of understanding of the viewpoints of the others. If all take a  
defensive attitude from the start and paint all their competitors with  
dark colours then there may never be any consensus. In typical  
political environments good poll information including approvals and  
ratings is thus a positive thing, but it may still be necessary to  
assume that strong competition is not uncommon in the actual election  
and prepare for that.

Voters may also understand that a society that makes consensus  
decisions may be a better place to live in than a society where the  
current majority always ignores the minorities. And people may vote  
for parties that support this approach. But also here, it may still be  
wise to allow the majority to decide when consensus decisions (that  
cover also the needs of the other side) will be made. In a way we are  
talking about a "benevolent majority" and the growth of a society  
towards away from a conflict driven mode.

>
>>> 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.

Yes, the good part of Range is in the satisfaction measurements. I  
think the strategy problems are very real in many environments, not  
just hot air. So one must be careful with 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!

It is quite common that campaigns for some cause try to find positive  
expressions on matters that they promote and less positive ones on  
matters that they do not want to promote. Also many other campaigns do  
the same. There can be of course different levels of fairness,  
misleading statements, cleverly tailored sentences etc.

>
> 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?

I haven't yet seen any good definition of a core support requirement.  
(In two-party countries there may be a good correlation with "the  
system as it is today". It is also an interesting question if the core  
support requirement is related to the intent of letting that single  
elected candidate or party take all power and rule alone vs. in co- 
operation with others.)

I also note that having lots of second (and third) preference support  
typically correlates strongly with having also reasonable amount of  
first preference support.

>
> 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

Surely Condorcet too.

> , 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.

There is a natural incentive to the two largest groupings to promote  
this kind of polarization. And a two-party system is a demonstration  
that such systems may also work reasonably well in practice.

Juho