[EM] IRV vs Plurality

[Abd ul-Rahman Lomax]

At 04:24 PM 1/14/2010, Terry Bouricius wrote:
>Response to Robert's statement...
>"I guess I still haven't heard a good justification for why the 
>Condorcet winner, if one exists, should *ever* be rejected as the 
>elected winner."
>...
>
>Imagine this scenario. ..

Wow! Let's see what Terry comes up with.

>A highly polarized electorate with a three candidate race.

Oxymoron, probably! "Highly polarized" normally would mean two poles, 
or factions, with nothing in between. But there are three candidates, 
so, I assume, there is a moderate in between. In a highly polarized 
situation, electing a candidate from one or the other poles is very 
likely to be highly disruptive and damaging, it can cause civil wars, 
in the extreme. In such a situation, a true moderate is needed. But 
Terry proposes a faux moderate, some kind of pretend moderate, 
perhaps, we don't know.

>Only two candidates are seen by the media and the public as viable, 
>with 49% favoring candidate A and 46% favoring B, and 5% favoring C 
>slightly over A. Most voters don't know much about C, but C has 
>carefully avoided alienating any constituency by only stressing his 
>likeability, rather than issues.

That might be exactly what this situation needs, because a strong 
winner from either side, given how evenly the town is divided, could 
be a disaster, leading to a lack of ability to maintain order and 
govern with the consent of the people. Terry has carefully avoided 
using an example which would be much more clear, where the middle 
candidate has much larger "core support" but still remains trailing 
the other two as to first preference. This moderate candidate has 
only very low core support.

Because of this condition, it is indeed legitimate to call this 
"highly polarized," the middle is very weak on its own.

>  However while the supporters of both A and B don't think much of C 
> they rank C second because they subscribe to the "anybody but X" notion.

Terry wants to deprecate that notion, but it could be a lifesaver for 
the town if they vote accordingly. From the conditions stated, C may 
very well be the best candidate, but there is an obvious risk. I'd be 
much more comfortable with a C that has managed to gain a bit more 
direct preference, C is going to have a terrible time, I'd guess, 
unless C can actually act to attract stronger support based on 
knowledge. A town as described needs much more than a good voting 
system, it needs public process to bring people together.

Note that this is obviously a partisan town, this town would not, as 
described, hold nonpartisan elections, or if it did, the voting 
patterns would not appear unless there was some clear marker of 
affiliation, such as names that reflect an ethnic group, obviously. 
What, then, happens to C? Is C a member of a tribe? And what is the 
reputation of that tribe? Have they served a traditional role as peacemakers?


>The A supporters all rank A>C>B, while the B supporters all rank 
>B>C>A and the C voters all rank C>A>B
>
>49 A>C>B
>46 B>C>A
>   5 C>A>B

The C voters are obviously partisan, then, leading me to think that C 
is just a subfaction of A. C isn't a moderate, in between, so the 
voting pattern makes no sense. Terry is proposing that the B voters 
are just plain stupid and don't know their benefit from a hole in the 
ground. But the B voters don't have any choice, really. They are 
outnumbered, 54:46.

On the other hand, let's make an assumption: the B voters aren't 
stupid. They do know a bit about C, and they trust him to be better 
for them than the A candidate. At least he's trying to gain their 
support! By being polite and diplomatic and avoiding offending them. 
The A voters vote for him because they know he's naturally more 
sympathetic to them, and they don't realize that they will win if 
they just vote for their favorite and leave it at that. In other 
words, the A voters *are* stupid.

You can come up with a lot of fascinating election scenarios if you 
assume that the voters are really stupid! And that assumption makes 
Plurality, which, folks, ain't such a bad system, under some 
conditions, look really bad. Plurality works with informed voters 
being the most common and voting for the best possible option. 
"Informed" means that they know well what is possible politically, 
and "best possible" doesn't mean "vote for your favorite, hang what 
everyone else thinks."


>In a traditional runoff or IRV, A would win over B, after C's 
>elimination by 54 to 46. I think that is a reasonable expression of 
>"the public will" though not the only possible one.

And A is probably the natural winner of this election if the voters 
knew how to vote. In traditional runoff, A and B would go into a 
runoff. A would then quite likely win, except for this little 
problem. Terril has stated the C votes, but not the involved 
preference strength, a typical omission. He's assumed the same voters 
in the runoff, but the B voters are voting for their lives, perhaps, 
whereas the A voters may be less strongly motivated. Perhaps. 
Probably he's right, though, with the given conditions. A has the 
advantage and will probably win the runoff. But that is a separate 
election, and applying the Condorcet Criterion to two elections is 
problematic. It's true that with IRV, A would win, but I highly 
question the assumption that this is the best outcome.

>
>With Condorcet,
>C would defeat A by 51 to 49
>and C would defeat B by 54 to 46
>
>Thus C is the Condorcet winner.

Yes. And game theory suggests to me that C is the best winner. But it 
depends on preference strengths, really. But if we assume that the 
ranks express equal preference strengths, what would we get if we 
look at the only relatively objective method of studying voting 
outcome quality, summed social utility or voter satisfaction. So:

49: A 2 C 1
46: B 2 C 1
5:  C 2 A 1

Sum of satisfaction indices (2 = maximum satisfaction, 1 = 
indifference, 0 = maximum dissatisfaction)

A: 103
B: 92
C: 100.
It's actually quite a close election. Range chooses A, violating the 
Condorcet Criterion, but only by a very small amount, 3 points, which 
is 1.5 votes.

Now, consider this from the point of view of the B voters. The 
victory for A, how serious is this for them? If they see this 
situation, and it should be visible as a strong possibility, if they 
have trusted analyst with any sense, and if it's serious and not 
merely the loss of an election, I'd think that they'd carefully check 
out C. Is C really a moderate who might save the day and avoid a 
disaster. If so, they'd alter their vote, and how they'd alter it 
would depend on the voting method. If it's Range, this much is quite 
likely: they'd max rate C, if the Range resolution was as low. That 
is not an insincere vote, it merely fails to indicate their 
preference for B. But if it's Bucklin they can have their preference 
cake and their safety vote as well, and in this situation, in the 
end, both their votes would be counted.

Will the C voters, say it's Bucklin, vote also for A? If so, really, 
if their preference for A is sufficient to elevate A up to midrange, 
to approval, they are faux moderates and there isn't much hope for 
the B people, they might consider if emigration is possible. 
Seriously, that is, if the political situation is such as to 
represent a real risk. They are outnumbered. But, more likely, in a 
real situation, they C voters are somewhat moderate. They might 
truncate as well. Some of the more extreme of the A voters, realizing 
what is going on, will likewise bullet vote, some may add C. The B 
voters are fighting for their political survival, they'd better get 
it together, and unite. So, back to Range, we'd have:

25: A 2
24: A 2 C 1
46: B 2 C 2
5:  C 2

Range result:
A: 98
B: 96
C: 126

The B voters could suffer some leakage, some lack of discipline, in 
their voting pattern, and still get a better result.

The reality depends on their preference strengths. What I showed was 
that with equal preference strengths, A was actually (slightly) the 
better winner. But in a polarized situation, there is another factor. 
I used normalized preferences and assumed C as midrange, etc, 
initially. Ideal amalgamation as to satisfaction of reasonable voting 
criteria occurs when voters use von Neumann-Morganstern utilities to 
vote, not absolute sincere utilities normalized to one full vote. 
(The vNM utilities are also normalized). That's what the B voters did 
in my second analysis, they modified their utility profile, not 
violating preference order to reflect electionp probabilities, 
putting their voting strength where it counted.

If I go back and look at the original utilities, how much overall 
satisfaction was lost by the B voters following this strategy?

The overall satisfaction index sum for C was 100. That for A was 103. 
As I noted above, the loss in overall utility for the society was 
very small. But to the B voters: we have a value for A of 0. And a 
value of C of 46. That is a very large gain for them.

Now, what will the B voters do if the method is IRV? It's simple. 
Vote for C. C wins.

This kind of voting discipline is very unlikely in settled 
situations, where losing an election isn't a disaster, where the 
major candidates are not really all that far apart from each other, 
compared to the extremes. But here Terry, to create a bad-sounding 
scenario, imagines a "highly polarized" electorate. If they are 
really seriously polarized, that likely means that the situation is serious.

>It is certainly justifiable to argue that C is the "rightful" 
>winner. But it is not unreasonable to say that C is not the 
>"rightful" winner, since 95% of the voters are highly dissatisfied 
>with C being elected.

Eh? That was stated, but not shown. The overall satisfaction loss 
from C being elected is very small. The example shows, not what Terry 
asserts, but 95% of the voters being indifferent to the result in the 
sense that it's (barely) acceptable to them or, for 5%, their 
favorite, whereas any of the other two results leave 46% or 49% of 
the electorate "highly dissatisfied."

Now, I could again write the estimated utilities to reflect what 
Terry now says:

49: A 100, C 1
46: B 100, C 1
5:  C 100, A 50? doesn't matter unless a majority at, say 50 or 
higher is required.

Satisfaction sums:
A: 5150
B: 4600
C: 591

Note that C is the condorcet winner from the ballots, still. And 
there is from an SU point of view no basis for electing C. Terry is 
certain correct that this example shows that the Condorcet winner is 
not always the best. But we need more information than is present on 
the ballots to show that. Basically preference strength information.

However, there is another factor in elections besides absolute 
utility sums. The problem with this election (as writ when Terry 
stated that 95% of the voters would be "seriously dissatisfied") is 
that there is no satisfactory outcome, they are all actually pretty 
bad, with C being the worst. My comment about elections like this is 
that they need another candidate. None of the above. Note that with 
Top Two Runoff with write-ins allowed, that's actually possible. 
Risky, perhaps, but if A and B are on the ballot, as we'd expect, 
suppose the B and C voters really realize the danger and seriously 
campaign for a new possibility. Better, they do this before the first election.

I'd say that what this society really needs is Asset, to create a 
representative body that can negotiate compromises that will be more 
broadly satisfactory than one side or the other getting its first 
preference at the outset. Real politics isn't a zero-sum game, 
outcomes are possible that raise everyone's boat. I'd never suggest a 
single-winner presidential system for a place like that described 
here. They would need a parliamentary system, and Asset would allow 
it to be fully representative, not depending on factional 
affiliation, though voters are likely to vote within their factions 
if they are that polarized. But then the factions can negotiate 
within the elected assembly, and it rarely is better to duke it out 
with an almost-majority, even if you outnumber them, than to find 
good solutions that may even be better than the initial preferences, 
or that are reasonable compromises when there is some approach to a 
zero-sum situation.

What goes around comes around. If the A faction realized it's in the 
majority (and it appears that more or less it is, with 54% 
realistically analyzed, the C faction being a subset of the A 
faction) and it starts to exercise careless dictatorship of the 
majority, it could be sowing the whirlwind for itself, a backlash 
comes as the dissatisfied B faction starts to increase its preference 
strength, to the point that it might support insurrection or other 
action that causes more damage than good (for the A faction and maybe 
for everyone: push people to the point where they think they have 
nothing to lose, they may do practically anything, even stuff that 
doesn't make sense.)

  This is where the Range voting utility advocates enter the fray. My 
point is merely that the Condorcet-winner criterion is desirable in 
most cases, but not the only legitimate, nor ultimate criterion.

We actually agree on that. What is the ultimate criterion, Terry? I 
don't think it's a truly difficult question. The ultimate criterion 
would be a combination of overall absolute utility maximization, 
modified avoidance of serious variation for anyone.

It's possible to approach these ideals, but, to be practical, we must 
modify "anyone" to "as large a proportion of the population as 
possible," or, stated the other way, minimizing serious variation to 
as small a number as possible. Let me explain what this means.

We have, as a society, two options. The first option, taking into 
consideration what has been called the heaven-hell scale of utilities 
(which I'm presuming, I am *not* claiming that we can actually know 
these utilities, I'm positing them, not calculating them), is the 
overall utility maximizer. However, there is a second option which 
does little damage to this, but a little. The heaven-hell scale 
includes a valuation on human life, because when a society makes 
choices, these choices have real effects. Spend less money on 
nutrition programs, kids die. But if the money spent on nutrition, as 
a possibility, takes money away from some other program that prevents 
other deaths, some choice may have to be made. We are not omnipotent, 
no matter how well we might vote.

The first option causes the death of some individuals, but a very 
small number. This is not a zero on the heaven-hell scale, for there 
are fates worse than death. But we can consider it a very poor 
outcome for those people. The second option, however, causes no 
deaths, but some loss overall, not impacting people as severely as 
death. That some people die is a "serious variation" for some 
compared to the effect on everyone else.

Now, considering this kind of variation might be difficult, and, as 
well, determining absolute utilities very difficult as well, if not 
impossible. However, by the careful study of how voting system 
amalgamate voter reports of their preferences, as inferred from 
posited utilities in simulations, we can optimize voting systems so 
that they really do take into account the collective intelligence of 
the society.

And we should use this information to guide us toward improving our 
collective decision-making processes. What do you think, Terry?

I'm talking here about the possible work of the Election Science 
Foundation, which would *not* be a promoter of Range Voting, in spite 
of the ideas of some, and how can I say that with reasonable confidence?

Well, the informal mailing list that is the manifestation, so far, of 
the ESF held an election of a steering committee, recently. 17 people 
voted. Eating our own dogfood, to use Clay Shentrup's charming 
phrase, we used Asset Voting. Believe it or not, I did not set this 
up, and I'd been inactive. I did, however, notice it and declared 
myself as a candidate. The system was vote-for-one, which works fine 
with Asset. Warren invented a more complicated version of Asset, 
probably too complicated for actual use! Now, the exact rules had not 
been determined, yet the Asset principle, that candidates "own" the 
votes they recieve and may recast them to create winners. 3 seats 
were being elected. Had I set this up, I'd have put clear rules in 
place in the first place. Clay did set up some clear rules, that made 
no sense, he's not been a serious student of Asset, but he did 
realize that the basic method was totally cool for creating 
proportional representation.

This was, to my knowledge, the first actual Asset election every 
held. I fast-forward to the result. I got 8 votes, Clay got 5 votes, 
Warren got 3, Sean got 2, and Raph got 1. Simple ballot. Who won?

It's obvious that if I wanted a seat, I deserved one. But what about 
the other two? Asset managed this with a brief period of 
consideration, practically no argument, something that otherwise 
might have taken with the normal highly inefficient process of 
everyone discussing something to death and dissatisfied particapants 
stopping reading the thing in disgust, etc. Believe me, I know it 
well, see it all the time on Wikipedia.

The steering committee: Myself, Warren, Raph. You would never guess 
this just from the votes, except for my election. *Every candidate 
consented to the result.* That is, in effect, a unanimous election. 
Don't try this trick with any other election method! And it is a 
trick. Asset isn't an election method, it is a method of gathering 
representation by incremental and intelligent amalgamation, with each 
action amalgamating or assembling a quota being purely voluntary and 
unopposed. Representation by choice, not by "election."

We didn't have any means to determine constituencies, specifically, 
but it doesn't matter. Collectively the three members do represent 
every member, by consent. I wasn't expecting it to be this good. Next 
time we run an Asset election, we'll have the rules in place, we 
didn't have a crisp definition of rules, Clay had set it up to be 
Plurality-at-large with only the Asset tweak of allowing vote 
reassignments before a deadline. However, holding eight votes, I was 
able to hold out for a little better, and Clay decided to transfer 
his votes to Warren, thus giving Warren and I equal transferred 
power, though I'd already handed off, provisionally, enough votes to 
elect Warren to him. Warren got as few votes as he got because one of 
the activities of the ESF might be helping fund research into voting 
systems, and he's a possible recipient of funding, well-deserved, I'd 
say, so he shouldn't be on the board of the ESF. But we weren't 
electing the board, and some members were confused about that. Warren 
probably shouldn't be on the board. Further, Raph is not a U.S. 
citizen, but there is nothing wrong with him being on the steering 
committee and maybe nothing wrong with him being on the board, we 
haven't done the legal research yet.

The ESF will support research into voting systems and the development 
and operation of educational programs on the topic of voting science. 
It will be a 501(c)(3) organization and will strictly avoid lobbying 
for any specific legislation, but it can and will provide testimony 
on the topic, and it's part of my own task to ensure that this isn't 
biased toward or against any given system. It will surely study 
Instant Runoff Voting, for example. How is it working, Terry? Does it 
live up to the promises? Is Center Squeeze some rare phenomenon, or 
does it actually crop up in real elections in the U.S.? You know the 
answer, I'm sure, but does the public? Does the public have any 
reliable information on this?

How about joining us, Terry? I'm sure your experience would be 
valuable. It's a googlegroup, no cost, no obligation, no commitment 
or endorsement implied by joining, and maybe you could help keep us 
straight. It's hard to recognize bias with respect to one's own point 
of view! I'm not sure of the method to join the group, but I was long 
ago given moderator privileges there and I'd be happy to add you on 
request if you ask for it.

http://groups.google.com/group/electionsciencefoundation

We are not FairVote. We use fair voting and study what makes voting 
fair and not fair, effective and not effective, with consideration of 
the purposes of voting, not just the math of it. But we also think 
the math is important, and so is real-world data. This is, after all, 
a science we are working with. Math and simulations and theory are 
nowhere near enough for a science.

I'm sure that political action groups will arise, including some 
operated and coordinated by members of the ESF, but the ESF, as a 
foundation, won't endorse them, and ESF won't have, as part of its 
activities, lobbying. The PACS are free to endorse ESF and support it 
if they like. Anyone who wants to support it may, and anyone may 
contribute their funds or knowledge or research, and ESF will attempt 
to consider it all.

By the way, I should add that I'm not officially representing ESF 
here, there has been no vote allowing me to do that, and I wouldn't 
write as I've written as a representative of ESF. ESF will be very 
careful avoiding justifying a perception of bias. I imagine that ESF 
may coordinate the availability of voting system experts to testify 
as requested by various bodies, but they will be testifying 
individually, in general, and ESF won't interfere with their freedom, 
though I doubt that we'd continue to support such witnesses if they 
provided deceptive testimony or acted uncivilly.

Just my opinion at this point. But this isn't just me any more, there 
are people itching to Get Stuff Done.