[EM] Range strategy pathological example (was Re: IRV vs Plurality)

[Abd ul-Rahman Lomax]

At 02:53 PM 1/26/2010, Jameson Quinn wrote:

>... a lot of hot air about "strategic voting" in Range.
>Here's the nightmare scenario:

Thanks for an opportunity to address this, it's a very common 
misconception about Range.

>True (normalized) utilities:
>20% voters: 10 Ader, 7 Bore, 0 Cush
>20% voters: 8 Ader, 10 Bore, 0 Cush
>20% voters: 0 Ader, 10 Bore, 8 Cush
>40% voters: 0 Ader, 8 Bore, 10 Cush

Okay, but there are several things not specified. One is voter 
knowledge. Are these blind voters who have no idea of what others 
think, or are they more like real voters, who do know the actual 
political situation more or less?

There is a very strange assumption that voters will forget that they 
are *voting*, which means exercising political power, and will 
instead mindlessly vote "true utilities." Consider this: in American 
elections, the candidates on the ballot are not the only candidates. 
Voters can write in any name they like, and with Range Voting, it is 
harmless, it does not interfere with their other votes, it has no 
effect at all. So let's include for each voter, 
AbsolutelyIdealPerfectCandidate. Hey, blows everone away! For 
example, the first line becomes

20% voters: 10 AIPC, 2 Ader, 1 Bore, 0 Cush.

But is anyone in their right mind going to vote that way? Now, 
consider Ader in this election. What's Ader's position?

>Bore is the CW by a 60/40 margin over the other candidates, and the 
>true Range winner (avg 8.4 vs Cush's avg 5.6).

Notice that Mr. Quinn did not even really mention Ader, but Ader, by 
affecting the normalization, has affected the supposed "true 
utilities." Why was that normalization chosen? The recommendation for 
Range Voting is quite the same as for Approval, with the possibility of tweaks:

Vote max or almost max for your favorite frontrunner.
Vote min or almost min for the worst frontrunner.
If there are three frontrunners, it gets a little more complicated, 
but that's not relevant here. It doesn't get much more complicated....
And as to non-frontrunners, do whatever you feel like, just don't 
reverse preferences.

Ader is 36% Range. Way down. In first preference, Ader is at 20% 
compared to 40% Gore and 40% Bush. So what will the voters think in 
this situation? It's pretty simple: they will know that the election 
is really between Bore and Cush, and they are not about to waste 
their vote. Here is what I'd predict with pure Range, which, by the 
way, I do not actually recommend for public elections, certainly not 
as a first step. I'd like to see Range *ballots* ASAP, but analyzed 
as Bucklin ballots, in a runoff voting context as a primary, with 
approval cutoff being explicit on the Range Ballot. Majority approval 
is required to win the election in the primary. I'll leave runoff 
details till later.

>However, if the Cush voters all strategically downrank Bore to 0, 
>then Cush wins (Bore's average drops to 5.4).

And if the Bore voters all drop dead of heart attacks before voting, 
same result. This is preposterous. Supposedly there is some disease 
called "utter stupidity" which falls only upon the Bore voters but 
does not at all afflict the Cush voters, who vote a perfectly 
*sincere* vote indicating that they really want to see Cush elected, 
and they are not at all worried about failing to give eight-tenths of 
their vote to the Ader/Bore pairwise election, because they know that 
it is completely irrelevant. They aren't going to waste their vote 
expressing their complete contempt for Ader!

Why, pray tell, does the intense stupidity afflict only the Bore voters?

A great deal of confusion has been created by shallow understanding 
of utility analysis in studying voting systems. Normalization, lest 
we forget it, is a *strategy* for casting a more powerful vote than 
is cast by using true utilities on a commensurable heaven/hell scale, 
which would probably lead most people to vote somewhere around 50% 
for all candidates! Rather, people, in voting, are making choices, 
and, in reality, people vote von Neumann-Morganstern utilities, which 
are normalized utilities modified by election probabilities, if they 
are voting rationally. People do vote for other reasons.

>Yes, there are potential counterstrategies.

Like voting intelligently?

>  But if I can construct a semi-plausible example where unanimous 
> strategy overcomes giant 3-2 margins (in terms of both Condorcet 
> and Range), then in real life, smaller margins in strategy could 
> overcome smaller real-world margins.

Let's not even get into the problems involved in "unanimous 
strategy." 40% of voters who have the discipline to implement a 
"unanimous strategy" could basically wipe the floor with everyone 
else if they want to.

The real situation here, if the votes are as modified by this 
"unanimous strategy." If I see a vote like A 0, B 8, C 10, I am going 
to assume that the voter will be *almost* perfectly happy with a C 
result. If that's not true, why in the world did the voter vote that 
way? But what is posited here is that the voters who voted that way 
will be pissed that the method took their votes at face value. It's 
like the FairVote "nightmare" scenario:

99: A, 100, B, 99
1:  A, 0,   B 100.

Wow: 99:1 by preference, but range is sum of votes 9900:9901, so, in 
spite of the "landslide" in first preference, B wins. However, I look 
at this and think, what would I mean with a vote of 100:99? I would 
mean that, sure, I have some barely detectable preference for A, but, 
in fact, I really don't care which it is, A or B. Note that the 
ridiculous extremity of this is only possible with high-resolution range.

Imagine this with approval:

99: A, B
1, B.

B wins. And this is absolutely acceptable and is actually used in 
certain public elections (multiple conflicting ballot questions).

>  And the reason I call it a "nightmare" scenario is that I believe 
> most people would find this result especially bad, since it 
> "rewards" the "sneaky" Cush voters who "take advantage of" the 
> "innocent" others.

But they aren't sneaky, they are voting sensible and in accord with 
what they want. I'm not sure I want voters to be "innocent" if that 
means "totally naive." Voting a Range election with the votes 
described is completely stupid. I certainly wouldn't do it, and I 
wouldn't want anyone to do it.

Now, lets look at this from another perspective. Make this election 
Range/Bucklin. It proceeds in rounds, starting with 10s, moving down, 
adding approvals when the threshold reaches the range vote for the 
candidate. Suppose it terminates, first, at 5, and if there is no 
majority, then there is a runoff. But who are the candidates? We 
would use, perhaps, the top two Range candidates. Votes at thresholds:

Ader, Bore, Cush, normalized votes first
10: 20, 40, 40
8:  40, 80, 60 Bore wins with 80% of the vote.

No Bucklin election is known where multiple majorities were found, to 
my knowledge, though it is certainly possible. This points out the 
preposterousness of voting the "true normalized utilities," straight. 
What is a real risk with Bucklin (as with IRV) is majority failure, 
there is no majority.

With the Cush voters voting sanely, every one else votes stupidly:
10: 20, 40, 40
8:  40, 40, 60. Cush wins. And why?

Because the Bore right wing (if I assume that orientation) put 80% of 
their vote into an irrelevant candidate pair, leaving only 20% of 
their vote for the Bore/Cush pair. They *approved* Cush at the 80% 
level, that is how they voted. And now you think they would be upset?

>  This would be especially divisive if there were already-explosive 
> ethnic or gender politics behind the division.

In which case I'd think they would not at all vote this way. Maybe 
the voters should try to understand what it means to *vote*. It's 
about making choices, not expressing sentiments. Range allows voters 
to express true relative preference, preference reversal never is an 
advantage. But it doesn't remove the responsibility for exercising an 
effective vote from voters.

For this reason, indeed, because of possible confusion about what a 
Range vote means, I don't recommend starting with Range Voting. I 
recommend starting with Bucklin, in fact. But, step by step, this can 
be converted to using a Range ballot, and once Range ballots are in 
use, not only will voters learn to use them with sensible strategy, 
but very valuable preference strength information will be collected.

A major step toward full-on Range voting will have been taken when 
being a Range sum-of-votes winner or maybe even average vote winner 
can get you into a runoff, even if you lose with a Bucklin counting 
method. But that's down the road. I'm not sure that Range without 
approval cutoff would *ever* be a desirable system, because of 
problems with normalization. But it is clearly the best ballot, 
collecting the most possible useful information, needing only the 
addition of explicit approval cutoff. In the example give, would the 
Bore voters have voted 0, 10, 8 if 5 had been the specified approval 
cutoff, this was an explicit acceptance of the election of Cush? And, 
then, supposedly, they would be upset later? Why?

Folks, we can't even get, yet, any jurisdiction to simply count all 
the votes (Approval, which should never be compared with more 
flexible voting systems, only with plurality or vote-for-one), much 
less to do it using a preferential ballot (Bucklin) or range ballot.

>Thus, to me, Range's problem with strategy is not merely "hot air". 
>Not that it's insoluble - for instance, a Range ballot with options 
>of only 0, 1, 998, 999, and 1000 would solve the strategy problem by 
>forcing all voters to use strategy (and thus would reduce to 
>Approval, with the advantage that it could be post-analyzed to find 
>a CW). There are other ways to fix the problem, too. And this one 
>disadvantage of Range should be weighed against Range's many clear 
>advantages. But it is a real problem.

No. Not real, because the scenario is utterly unrealistic unless 
voters have somehow been deceived into thinking that they should vote 
stupidly. From the utilities given, and the election context, I'll 
predict real voting patterns:

>True (normalized) utilities:
>20% voters: 10 Ader, 7 Bore, 0 Cush
>20% voters: 8 Ader, 10 Bore, 0 Cush
>20% voters: 0 Ader, 10 Bore, 8 Cush
>40% voters: 0 Ader, 8 Bore, 10 Cush

Frontrunners, by large margin: Bore and Cush.
Basic strategy, vote max or close to max for preferred frontrunner, 
vote min or close to min for worst frontrunner. Never reverse 
preference, and with Range 10, probably safe to preserve preference. 
(With Range/Bucklin, completely safe, I'd say).

20%: 10 Ader, 7 Bore, 0 Cush ... I left Bore at 7 because Ader is 
outlier, minor candidate and supporters may really want to show 
significant preference.

20%: 8 Ader, 10 Bore, 0 Cush ... No reason not to vote normalized 
utilities here, because the minor candidate is intermediate.

20%: 0 Ader, 10 Bore, 1 Cush ... Actually, the "1" for Cush is 
probably an overestimate. I'd expect these voters to bullet vote, really.

40%: 0 Ader, 0 Bore, 10 Cush ... These voters, I'll accept as "more 
fanatic." In reality, though, all the normalized 8 for Bore means is 
that they detest Ader.... Bullet voting will be normal for most 
voters in a two-party context. Somehow we seem to miss this!

Result: Ader 36%, Bore 54%, Cush 42%. Bore wins.

Don't imagine that you will get good election results with voters who 
cast votes that they would regret! And that is exactly what you did, 
imagine that the Bore voters would cast fundamentally weak votes, and 
that they would then dislike the results, whereas if they had 
expressed with their vote that they would dislike the results, they 
wouldn't have gotten the disliked result!

"Dislike" means "by comparison with reasonable expectation." It's 
relative, not absolute.

The "nightmare scenarios," all that I've seen, involve utterly 
unrealistic voting strategies, with voters who are then shocked that 
the method takes their votes as written.

Now, what if this is a zero-knowledge election? I'll have to ask, is 
it zero-knowledge for all voters, or just for the Cush voters? If the 
latter, do we imagine that we will have a voting system that pits 60% 
ignorant voters with 40% smart voters, and somehow the ignorant 
voters are going to prevail? No, in real elections, no party has a 
monopoly on ignorance or intelligence, though there certainly can be 
variations.

I wonder, did the Nader voters in 2000 know that by voting for Nader, 
they might be allowing Bush to win? I think it is crazy to assume 
that they did not know this. They may certainly not have known how 
serious an error it could be, but at the time, they accepted the 
risk, and Nader was telling them that it didn't matter. It didn't 
matter that the next president would be able to pack the Supreme 
Court, and all the rest of it didn't matter, Tweedledum and 
Tweedledee, after all. Basically, in Range terms, they had low 
preference strength between Bush and Gore. Do we imagine that Range 
Voting would fix this? Why? What if they vote that way?

Range voting is, indeed, an ideal method for amalgamating preferences 
to determine a social ordering, and it's been shown to be the only 
system that satisfies a set of Arrovian criteria modified to be 
applicable to equal-ranking systems and expression of preference 
strength, but to do this, the voters are presumed to vote vNM 
utilities, which are normalized personal utilities modified by 
election probabilities. I.e., the way people actually make choices in 
the real world (rational choices, that is, there are also other 
forces at work).

Which do you prefer, $1 or $10? Okay, three choices in an election, 
A, B, C. With A, you get 0, with B you get $1, with C, you get $10. 
However, other people have different values for each choice, and your 
estimate is that the real choice, by far, is the A/B choice, the C 
choice is very unlikely. Range election. How do you vote? If it is 
approval, pretty obvious: you vote 0, 1, 1. But in high-resolution 
range, you might vote, say, 0, 0.999, 1.000. It would depend on your 
estimate of the probability that your vote would affect the outcome. 
If you are a gambler, though, you might vote 0, 0, 1. After all, you 
only lose a dollar. And gamblers, in the long run, lose money, unless 
they play the odds accurately.