[EM] The worst about each system; Approval Preferential

[Abd ul-Rahman Lomax]

At 05:28 PM 5/27/2010, Jameson Quinn wrote:


>Correct strategy in APV when the two frontrunners are ideologically 
>distinct is to disapprove one and everybody worse, prefer the other 
>and everybody better, and approve everybody in between.
>
>
>Eh? That forces favorite betrayal, doesn't it?
>
>
>No.

Okay, by "approve," you must mean "approve or prefer." This is also 
"correct strategy," i.e., maximizes expected outcome, with any 
Bucklin method I've seen. The more a third candidate approaches 
parity with the others, the less obvious it becomes. With a runoff as 
a possibility when there is majority failure, it is possible to defer 
making the decision to approve a frontrunner, such that one will only 
do it if the preference strength for more-preferred candidates is 
low. With three major candidates, the probability that voters have a 
good understanding of all three goes down. Most voters will still 
have a first choice. I can say that when I come to a race on a ballot 
where there are only unknown candidates, I skip it, unless I know of 
a good write-in.

And I recommend that behavior. If one is not willing to defer the 
judgment to the rest of the electorate, one can write in "Someone 
Else, 27 West 57th Place, Nowhere, MA." (Local rules ask for an 
address for write-ins and the clerks tend to disregard write-ins 
without an address. But they are still reported as "write-in," and 
still for part of the basis for a majority, and are therefore a vote 
against all other candidates.)

Wo what this strategy does is to, by default, seek a majority for one 
of the frontrunners. It's likely to do so unless there are more than 
two frontrunners. The supporters of minor candidates normally know 
that they are minor, so they are the most likely to add additional approvals.

>"Correct strategy" presumes that a particular goal is "correct." 
>What is it, in this case? Presumed here is an assumption that 
>ideology is the issue.
>
>
>I give a more precise and general definition below for the shorthand 
>"ideology", which makes your objections moot. Perhaps you should 
>finish a paragraph before writing several in response to the first sentence.

Your "should" presumes a behavioral model here which is inaccurate. I 
use the comments of others as grist for generating my own comments. I 
frequently respond as I read. I risk sticking my foot in my mouth. 
You get to see my reactions from *before* you have completed your 
argument. Some of them will be "moot," in which case you can thank me 
for effectively agreeing with you. I.e., for making an objection, 
say, that you would see as needing argument, which you supplied. My 
goal is discursive, not generally polemic. When I move into polemic 
mode, you will see my responses become far shorter. These are, for 
me, discussions, explorations, not finished argument in a debate. As 
this proceeds, though, for me, the issues become clearer, and the 
background generated becomes part of the foundation of my continuing 
positions (or shifts those positions).

This isn't for everyone. It is for me, and for you and others if you 
care to participate or read. If you don't, no obligation. There is no 
presumption, with mailing lists, that anyone has read anything, 
unless they respond.



>If voluntary and honest. But one dishonest strategic expression can 
>"poison" a number of honest expressions. Moreover, even semi-honest 
>strategy creates two classes of voting power - strategic and 
>nonstrategic - which hurts legitimacy.
>
>
>I would encourage all voters to vote strategically and honestly. In 
>a Bucklin system there is no advantage to dishonesty that is worth 
>the risk. I.e., from a game theory point of view, net zero or 
>negative expected gain.
>
>
>I happen to agree. But some voters might overestimate their capacity 
>to predict behavior, and the fact that they're wrong doesn't stop 
>the harm they do. In my system, where there is never more and almost 
>always significantly less payoff from dishonest strategy, this is 
>less of a danger.

The harm they do is mostly to themselves, not to others. The supposed 
rational strategy for these voters, if based on overestimation of the 
accuracy of their knowledge, results in their exclusion from the 
decisive electorate. In other words, the method will maximize the 
utility of everyone else. Alternatively, if they cast a 
"turkey-raising" vote, we do have the possibility that a majority 
raise that turkey, and it becomes the national flag. When a majority 
makes a mistake, it's done until the next opportunity. It is 
impossible to prevent the majority from making mistakes through 
voting systems! If a majority want to vote with a stupid strategy, 
and turkey-raising with runoff methods is, at least, very dangerous, 
they can do it.

I find it practically inconceivable that a normal electorate would do 
this in large numbers. So such a strategy can only afflict small 
groups, and affect close elections. In Lizard v Wizard, did some of 
the voters favoring the Lizard vote for the Wizard in the primary? 
It's not impossible, but awfully unlikely for there to have been more 
than a scattering. Most voters were, I'm sure, just figuring out whom 
they most supported. The Lizard had a strong political base, and one 
which would be *very* opposed to the Wizard. No, this was just 
classic center squeeze, and if the method had been Bucklin, Roemer 
would have leapt into first place, and quite probably would have 
gained a majority in the primary, finishing the election. If not, it 
would have been Lizard v. Roemer in the runoff, and Roemer would 
probably have creamed the Lizard. Or not. The problem woudl be 
preference strength. The runoof that was Lizard v. Wizard had huge 
turnout, exceeding the primary turnout (which was a general election 
primary, as I recall). Lizard v. Roemer would have been much lower 
turnout, because fewer would have cared so strongly.

(For those who don't know this election, I recommend Poundstone, 
Gaming the Vote. The Lizard was a corrupt Democrat, and the Wizard 
had been the Grand Wizard of the KKK. Because the Wizard was on the 
ballot, turnout among people inclined to support the KKK in some way 
probably turned out heavily in the primary. In the runoff, support 
for the Wizard barely increased, and the Wizard had been in second 
place in the primary anyway. There was a similar effect in the French 
presidential election which is also often given as an example of 
center squeeze. Extremist candidate, probably high turnout for 
supporters in the primary, same turnout in the runoff, somewhat 
increased because now The Forces of Truth and Justice finally have a 
chance! -- but basically done. In ordinary runoffs, a dark horse can 
come up to second place and now has a chance and this is where runoffs shine.


>Anyway, you didn't respond to my critique of semi-honest strategy. 
>In APV, naive human nature strategy is closer to being the same as 
>optimal strategy, so the difference in voting power is less. This 
>means more legitimacy.
>
>This is important: the math hasn't been done, but my intuition here 
>is that the rational strategic Bucklin ballot is a Range ballot with 
>these restrictions: the candidates are divided into two sets, 
>approved and non-approved, and range ratings are best as sincere 
>ratings *within these sets*.
>
>
>I vigorously disagree. The rational strategic Bucklin ballot is, to 
>first approximation, an approval ballot. In some cases (which I 
>don't quite have a handle on) it might be rational to move a single 
>candidate down from maximal to minimal approval, or to add a minimal 
>approval to a single candidate who would not have made the cut under 
>approval. Intermediate approved rankings are never rational if all 
>voters are purely rational, though if there are some honest voters, 
>it may become rational to use intermediate approvals occasionally. 
>Unapproved rankings besides the bottom are used for turkey-raising if at all.

A Bucklin ballot is a kind of approval ballot, yes. But it allows 
ranking within the approved class, and rational strategy for the 
ranking is sincere Range equivalent, within the approved range. That 
range can be narrow (one candidate fits in it) or broad (many 
candidates, but all of which the voter is willing, under the 
conditions, to approve. That's a separate issue, how to decide who 
fits into the approved class.) The argument about "intermediate 
rankings" would apply to Range voting as well, and it's bogus there 
as well as here. It's based on shallow analysis that makes 
assumptions about what voters want that aren't accurate as to real 
voters. The addition of unapproved rankings to a Bucklin ballot is a 
new idea, and should not be mixed up with criticism of basic Bucklin, 
including Bucklin/runoff as a general proposal, replacing top two runoff.

Note that if we think that the rational strategy for ranking is 
"approval style," no intermediate rankings, we must, logically, think 
the same for Range voting. I've done the math on that, you know. 
Whether or not pure approval strategy is best is an issue dependent 
upon voter knowledge as well as voter preference strengths and the 
difficulty of making decisions. Decisions in the presence of high 
roundoff error become more difficult, not easier. I.e, if I have 
trouble deciding whether to put a candidate in top-approved or 
bottom-approved, I can quickly resolve this by putting the candidate 
in middle-approved. The strategic difference would be small, thus the 
ability to make an intermediate decision is helpful.

Essentially, the middle-approved rating, which Mr. Quinn thinks 
useless or even harmful, has a real function to assist voters in 
categorizing. Ini general, the arguments for limiting expressivity 
are similar to the argumewnts for Approval vs. Range. But Range 
*allows* voting approval style, if the voter thinks that easier!

This qualification "if there are some honest voters" is useless. Most 
voters are and will be relatively honest within customs and their 
understanding of possibilities. Most voters who would greatly prefer 
an unnamed candidate for an office do not therefore write in that 
name unless they have reason to believe that others will do so, or 
they really do have no significant preference between the candidates 
on the ballot.

Middle ranks were used. Mr. Quinn thinks, apparently, that the voters 
were strategically stupid. Okay, if that's true, they will learn and 
usage of the middle rank will decline. I do predict some level of 
decline, but it will not stop happening.

Note that "approval" (distinct from "preferred") is really "extra" 
from this black-and-white strategic viewpoint.


>That's why adding levers and knobs to your voting system is 
>dangerous if they can be used strategically with impunity.
>
>
>I've seen no cogent example of this. In evaluating strategy, I'd 
>encourage Mr. Quinn and anyone else to *start* with utilities.
>
>I do.

But he has not disclosed them, numerically. He has, I'd guess, some 
seat-of-the-pants concept of utilities and how they motivate voters. 
But by not being quantified, it can then easily lead to contradictory 
conclusions that are not recognized as such. A lot of error in 
analyzing voting systems is caused by this.


>Voters will bullet vote, commonly. It is a rational and sensible and 
>*sincere* strategy, properly understood.
>
>
>Absolutely true in many, but not all, cases.

I didn't assert that it was for all cases. However, I'm quite 
suspicious of facile assumptions that a voter will "really" approve 
of A, but will not vote for A becasue the voter prefers B. To me, 
this means that, because of the presence of B, the voter does *not* 
approve of A, and the voter will only approve of A relative to 
another option, C. Approval drove the ranked voting anaysts nuts, 
because ranking can be imagined to be a quality of the candidates, 
whereas approval is not. In an election with many candidates, there 
are very many possible sincere votes. Bullet voting is sincere, it is 
a sincere and accurate division of candidates into two classes, with 
every candidate in the approved class being preferred to every 
candidate in the unapproved class.

Thus, I'll claim, unless it's just a plain mistake, bullet voting is 
always sincere. This would take us into the old debate about whether 
or not Approval Voting satisfies the majority criterion.

>  I'd guess that mostly it's rational and sincere; sometimes it's 
> rational and insincere; and rarely it's irrational and sincere.
>
>Mr. Quinn's proposal is indeed simpler,
>
>
>Simpler; and better at harmonizing naive, individually optimal, and 
>socially optimal strategies. Both are important advantages.

So we "treat" naivety by hobbling evreryone else?

>  That is, a solid majority coalition might elect its more radical 
> member, not the centrist. "Solid majority" means that the median 
> voter is a member of that coalition, supporting the "radical" on 
> that side over all other candidates. Unlike closed primaries, if 
> there's a majority but it's not solid, the centrist from that side 
> is probably elected.
>
>
>In the example shown, there was a drastic difference between the 
>winner and loser.
>
>
>And it was an artificially-constructed example, one which both the 
>naive and the correct strategy (which are the same in this case) 
>would tend to discourage from ever happening.

In other words, you are attempting to prevent stupid voters from 
negatively influencing the outcome, while still helping them to get 
what you think they want.


>If you're relying on it working, people will manipulate it, and that 
>manipulation will be arguably biased; that is, one side will 
>arguably be doing it more than the other. (Whether there truly is a 
>bias or not doesn't matter; the mere appearance of bias undermines legitimacy.)
>
>
>What I have not seen is a manipulation scenario that makes sense 
>*for the manipulators*, when risks are considered along with 
>possible gain. As I've mentioned, though, it is possible that with 
>full knowledge, any voting system can be "manipulated," but, if it 
>is a utility-maximizing system, the "damage" is limited to the 
>voting power of the manipulating faction. It's, in fact, 
>questionable if it is damage at all, and if that faction directly 
>uses its power, it would not be bothering with "turkey raising" as 
>Mr. Quinn proposed.
>
>
>Again, want to bet? You program your agents to vote your strategy, 
>I'll program mine to take them to the bank. All agents have random 
>preferences, except that each candidate is either "Jameson-style" or 
>"Abd-style", with a small bonus to the utility of all respective 
>agents for that candidate. We can do any reasonable set of 
>pre-election imperfect information, though of course zero 
>information is by far the easiest to program for.
>
>Otherwise, this is just hot air.
>
>
>I know that Bucklin *did* work. I have no reason to believe that it 
>wouldn't continue to do so. The changes I'm suggesting simply 
>improve it to reflect modern voting system theory, they are not drastic.
>
>The "manipulations" as designed would be somewhere between difficult 
>to impossible. Mr. Quinn did not show an exact scenario that 
>reflected how the method would actually work. Basically, it's 
>possible that a faction of voters, speaking roughly, could improve 
>results, from their perspective, *a little*, using a complex 
>strategy that could backfire, easily. Many theorists have proposed 
>voting strategies that were like this. In fact, serious voting 
>strategy, that requires voters to vote with reversed preference, 
>seems to be quite rare, that we would see it in nonpartisan 
>elections seems vanishingly possible, to impossible. The strategist 
>is asking voters to state on the ballot what they don't believe.
>
>As I've mentioned before, if my favorite candidate suggested that to 
>me, the candidate would no longer be my favorite.
>
>
>Ever heard of Limbaugh's "operation chaos"? It's not the candidates 
>you should worry about, but their loose-cannon allies.
>
>Thus promoting a turkey-raising strategy, in this context, would be 
>very hazardous. And I doubt that voters would do it individually. 
>This is a red herring.
>
>The basic error that Mr. Quinn makes is in assuming that bullet 
>voting will be a natural and practically universal strategy.
>
>
>Where on earth did I say that? In fact, I said several things which 
>contradict that: that Bucklin would encourage (strategically 
>misguided) extra ranks, and that correct strategy would find a CW in 
>one round if non-supporters cared about the distinction between the 
>two frontrunners.

You have not established that they are strategically misguided, then 
you build further assumptions on top of that. If you could show that 
middle ranks were contrary to the interests of the voters, should 
they use them, you would have a case for rejecting them. Unless it 
happens that "contrary to the interests of the voters who use them" 
results in better social utility. In other words, these voters by 
being "foolish" are helping the society to make better choices. I 
wouldn't call that foolish at all. I'd call it beneficial and for 
voters to do it, truly altruistic, not foolishly altruistic. This is, 
in fact, the general debate over Range voting, and we have good 
reason to believe -- and I have mathematical reason to believe -- 
that even a few voters voting intermediate ratings causes the overall 
performance to improve. Even one, in fact. It dithers the result.


>
>Definitely, bullet voting will be common. It's common with IRV where 
>it's allowed. It's a sensible, rational strategy for a voter without 
>sufficient information to do more than vote for their favorite, and 
>Lewis Carroll invented Asset Voting to enfranchise these voters with STV.
>
>Then, to the contrary, he posits some clever, conniving strategy
>
>
>Oh, I get it, calling your system design a "trick" (later clarified 
>to mean not evil but unstable) is not fair, but calling mine a 
>"clever, conniving strategy" is OK.

No, that was not the system design, it was the turkey-raising 
strategy, and I think you agree that this is not exactly 
"straightforward." It's possible to do it in Bucklin without Favorite 
Betrayal, which isn't true with top two runoff. But that's no 
improvement from the point of view of sincerity.


>  [...]
>Let me list the ways I find my proposal better than yours, in order 
>of importance.
>
>1. Simpler to explain.
>2. Naive, rational, and socially-optimal semi-honest strategies are 
>closer to each other.
>3. My system has stronger reasons not to use dishonest strategies 
>(turkey-raising).

Okay, let's work on explanations, ballot instructions. Plurality has 
the simplest ballot instructions. Approval next to that, I'd say. 
Ballot instructions, however, don't include "strategy." I've seen an 
exception, where it was claimed in the proposed Vermont IRV 
legislation that adding a lower ranked vote could not hurt your 
more-preferred candidate's chances of winning, and that was a 
mandated ballot instruction. And it was false. Way to go, Terrill! (I 
think he wrote this one, in the time he put it up.) That's because a 
true majority was required. And if there was no majority, the top 
three were tossed to the Vermont legislature for decision. So by 
ranking your second choice, you could cause the election to complete, 
whereas if you didn't do that,  there would have been no majority and 
your candidate would have had a chance. (But as the third of the 
three in votes, well, it better be center squeeze!)

The second reason is an argument for plurality, taking it to the 
extreme. Or, then, for Approval. Or, then, for Range 2. Etc. There is 
a point where additional range resolution provides declining benefit, 
but Range experts like Smith want to see high-resolution range, at 
least Range 99 or 100. It's clear that lowering Range resolution 
causes loss of social utility, unless, of course, everyone bullet 
votes. But we know that Range, with mixed strategy, is better than 
Approval. (Approval is Range 1).

>You're arguing against reason 3 by saying your system's 
>anti-dishonest-strategy properties are strong enough. You may be 
>right. I still prefer to be doubly safe. But that's my weakest reason anyway.

Turkey-raising strategy would apply to two-rank Bucklin or even 
simple Approval, if a runoff is required with majority failure, and 
especially if it's a naive top-two runoff. It gets really difficult 
with top three, because the goal, to knock the likely winner out of 
the runoff, gets much more difficult. That likely winner is really, 
in Bucklin, quite likely to win the primary. To knock him or her down 
to third place is hard, but not impossible, I'd say. To fourth place, 
it gets ridiculously difficult for a strategy that is dicey and 
difficult to promote in the first place, you can lose support just by 
advocating it.

>What are your system's advantages? To me, it's a lot of rules - for 
>nothing that my system can't accomplish using a nonbinding poll and 
>a write-in runoff.

Don't confuse the basic system with tweaks that are possible later 
improvements. While I'm proposing is basic Bucklin, three-rank, with 
only the no-overvoting rule completely tossed from all rounds, as a 
replacement for top two runoff. I'm proposing further refinements for 
later implementation if justified by the already-good ballot data 
that would be collected. I've arranged them in a hierarchy of precedence. So:

1. Context: jurisdiction with top-two runoff.
2. Proposed first reform: Traditional (Duluth) Bucklin primary, with 
only the rule requiring ballots to be disregarded in an overvoted 
rank or lower -- which only affects first rank and second rank, since 
original Bucklin allowed unrestricted voting in third rank already. 
This is actually simpler to implement than Duluth Bucklin.

2a. Options: top three runoff, Bucklin runoff. Or top two runoff, 
write-ins allowed in the runoff, Bucklin runoff (but maybe two-rank). 
Less preferred by me: simple top two plurality runoff.

then

3. Add disapproved rank for data collection. The ballot is now a 
Range 4 ballot, straight, with explicit approval cutoff at midrange. 
(Actually, it treats midrange as minimum approval.)

4. Use Condorcet analysis of the ballots to make the method guarantee 
that an expressed Condorcet winner makes it into the runoff. In this 
event, the runoff should be plurality with only two candidates 
allowed, or a condorcet compliant method, there are various 
possibilites that could exist and still retain the benefits of 
(almost complete0 social utility maximization. Other rules might be 
developed, based on analysis of election history, that could avoid 
unnecessary runoffs.

5. Increase the range resolution if needed. It's prossible that 
performance improves a bit to the point where all candidates can be 
fully ranked, and even beyond that point. (Even though Range 2 allows 
full ranking of 3 candidates, performance increases when more ranks 
are allowed, because then full ranking can be done *and* better 
expression of preference strength is possible.)