[EM] Cloneproofing Random Pair and Random Candidate?

[Abd ul-Rahman Lomax]

At 06:25 PM 4/4/2013, Jameson Quinn wrote:


>2013/4/4 Abd ul-Rahman Lomax <<mailto:abd at lomaxdesign.com>abd at lomaxdesign.com>
>At 01:54 PM 4/4/2013, Jameson Quinn wrote:
>
>Hay voting seems to have been invented to encourage the expression 
>of sincere utilities, as distinct from von Neumann-Morgenstern 
>utilities, and there is a whole practically knee-jerk assumption in 
>voting system theory that "strategy" is "bad."
>
>You've made that assertion, that people are looking for low-strategy 
>methods only out of an inherent aversion to strategy, before; and I 
>disagree. There are several problems people could have with 
>strategy, and different people (theorists) focus on different ones:
>1. Some say it's inherently bad because it's dishonest. (I don't care).
>
>
>Right. However, before Brams proposed Approval, "strategic voting" 
>meant reversing preferences, and Brams proclaimed Approval as 
>"strategy-free." So a *different meaning* was invented so that 
>Approval voting could be asserted to be "vulnerable" to strategic voting.
>
>
>That's not quite true. Gibbard's proof said "honest voting can be 
>any single ballot you want to define it to be; I don't care. 
>Strategic voting is any ballot which differs from that." So for 
>approval, you can (and people have) defined honest voting to be 
>bullet, anti-bullet, average utility cutoff, approve-half, intrinsic 
>arbitrary cutoff, and others. Any of those definitions are kosher, 
>but Gibbard's theorem says that none of them can be always 
>strategically correct.

That is a different issue. Without going through a formal proof, 
consider any election by any method, that does allow me choice and 
influence. I know -- say I'm psychic -- how everyone else has voted. 
But before this, I defined my "honest vote." And I see that two other 
candidates than my favorite are tied. The method requires a different 
vote than my "honest vote" in order to influence the outcome. I don't 
see how a single "honest" vote could also be strategically maximal. 
However, often lost in discussions of strategy is cost and benefit. 
In real life, we don't know the other votes so accurately. We make 
decisions based on averages and expectations, and a "dishonest" vote 
generally has a potential cost, and a "semi-honest" vote also a cost, 
compared to what might be called "full disclosure."

I don't know what Gibbard actually wrote, I'm depending on the above 
description. Basically, if a single ballot can shift the outcome, 
then that the requirement that the ballot consider, for example, 
possibly irrelevant alternatives -- such as all possible write-in 
votes -- in order to be "honest" -- seems impossible to meet with a 
deterministic system.

I see the effort to eliminate "strategy" from voting -- when it 
covers "semi-honest votes" -- which are essentially choices to 
approve or equal-rate sets rather than individual candidates -- as 
attempting to eliminate social consciousness from voting.

>
>The argument went like this. Supposedly a voter *really* approves of 
>both A and B, but wants A to win, so the voter "strategically" 
>bullet votes for A, the dishonest, greedy thing that he is. The 
>argument assumes that there is such a thing as absolute approval. In 
>fact, approval, the ordinary process in life, depends on context. 
>What I would approve of in one context I would be disappointed with 
>in another. It depends on my expectations. And "expectations" are 
>strategic considerations, i.e., what I think I can get. I'll vote to 
>maximize my expected return, and this is what we actually want 
>voters to do in Approval. But there are also other considerations. 
>If the voter bullet votes, the voter fails to participate in the 
>other elections.
>
>Approval can be a difficult decision. Bucklin makes it somewhat 
>easier, but there is still the ultimate approval (i.e., in the 
>lowest approved rank). Runoff Bucklin can make it even easier, there 
>will be a little more tendency to bullet vote, unless voters want to 
>avoid the burden of a runoff. And they can make the choice of 
>whether or not to vote in a runoff later. Depends on how much they care!
>
>
>2. Widespread strategy can have a disastrous impact on utility/BR. 
>(Think Borda, where this phenomenon is pretty well-documented, at 
>least anecdotally.)
>
>
>Uh, strategic voting in Borda involves preference reversal. That's a 
>different animal. A system that rewards preference *reversal* is a poor system.
>
>
>Forget the Borda example. The point is, even semi-honest approval 
>strategy can bring a social utility penalty, as Warren's original BR 
>calculations showed. This is why a Bucklin system like GMJ could in 
>practice have better BR/social utility than Score.

Please acknowledge the point. Is that a "disastrous impact"? Yes, 
*inaccurate estimation of probabilities* by voters can cause some 
loss. But not, with Approval, generally, a disastrous loss. I.e, you 
prefer A to B, but because you think A can't win, you also approve B. 
And then B wins by one vote over A!

You avoided the maximum disaster, the election of a candidate much 
worse, generally.

This can happen with *any system*. The cost of semi-honest voting is 
limited by the preference strength between approved candidates, in 
the equal ranking direction, and the possible loss of the omitted 
approved candidate to another.

I agree that Bucklin may have better BR than Range, under some 
conditions. But my suggestion is to hybridize systems, and runoff 
voting provides the opportunity.

Bucklin is particularly attractive because it simulates, quite 
reasonably, a series of repeated elections with voters lowering their 
approval cutoff, gradually, in order to complete the election. And 
then with a runoff, they can recalibrate, with knowledge of how others voted.

Using a Range ballot, the ballot and the process become more 
efficient and detailed.



>(Borda becomes an excellent system if equal ranking is allowed, and 
>empty ranks. Essentially, it's Range.)
>
>No, the kind of "strategy" I'm talking about is adjusting 
>*preference strength expression,* that's all. In the extreme, down 
>to zero. *Not* preference reversal as in Borda.
>
>
>2a. If different factions have different inclination or capacity for 
>strategy (for instance, due a take-no-prisoners attitude or better 
>access to polls) it could lead to "unfairness". This would impact 
>legitimacy as well as utility/BR, and the mere whiff of this could 
>be enough to cause a system to be repealed.
>
>
>Uh, intelligence and knowledge are rewarded? Quick! Who are these 
>people so we can stone them!
>
>
>Intelligence, knowledge, and ruthlessness. If strategic voting has a 
>social utility cost, however mild, then it is antisocial behavior, 
>however mild.

So partisan political behavior is antisocial? While I'd agree, to a 
degree, it's an extreme position. It's like saying that competition 
is antisocial. Can be! But we also *use* it as a social device.

>  Many people will feel that shouldn't be rewarded, and your sarcasm 
> isn't going to change their mind.

What's "that"? This discussion is floating in the air without examples.

>  If that "many" is a majority, they could repeal the system, and 
> you'll regret that, even if you never regretted the supposed unfairness.

Why would I regret it? You seem to imagine me as the "strategic 
voter," as if you think I'm identifying with him or her. It would 
seem to me that voting in a manner that offends people so much that 
they revise the system to disempower *me* would be not very 
"strategic." Kind of stupid, actually, wouldn't you think?

I'm not sure that I've seen *any* convincing example of strategic voting.

One allegation comes to mind. When Bucklin was being proposed in San 
Francisco, one of the debate points was that Bucklin had elected a 
Socialist, and it was claimed that everyone knows that Socialists 
will only vote for Socialists, so the Socialists voted for their 
candidate, whereas the nice, collaborative Republicans and Democrats 
also voted for the Socialist at lower preference, so he won.

I.e., selfish voters, bullet voting. Except it probably didn't 
happen. And it didn't fly as an argument in San Francisco. To get rid 
of Bucklin -- which passed by referendum -- took serious shenanigans 
by the Board of Elections, a blatant political maneuver even more 
obvious than what happened in Minnesota.

I can see the headlines: "Voter casts vote attempting to maximize 
personally desired outcome." I'm sure we are all shocked that anyone 
might do that.

>It is not pleasant to have to wonder if you're being taken advantage of.

Of course not, and people who readiy imagine that are generally miserable.

>  Even the most sophisticated strategists will have some niggling 
> doubts that there might be some yet-more-sophisticated strategist 
> out there who will take advantage of them. I enjoy a game of 
> Diplomacy as much as the next geek, but that's not what voting 
> should feel like.

With what system? What the hell are you talking about, Jameson? I'm 
active proposing the simplest, easiest-to-vote, straightforward 
voting systems possible, consistent with actually empowering voters. 
Plurality is simple to vote, until one realizes that the simple vote 
can readily be useless.



>No, this is basic. If a voter has clear knowledge of how others will 
>vote with any system, they can cast a maximally effective vote. The 
>easiest way to understand this is to consider that the knowledge is 
>so complete that it is as if they are the last voter, and they know 
>the results so far. So their vote is either useless (and they might 
>not even bother) or their vote can change the results the way they want.
>
>If a system is repealed because knowledgeable voters can vote more 
>effectively, and because this is true for every system worth 
>considering, to some degree,
>
>
>No it isn't. Under MJ and, even more so, SODA, a naive and 
>cognitively-simple "honest" vote is as good as the best strategy in 
>most realistic circumstances. Not all, but most; and "most" is good 
>enough, because that means that in most cases you can prove to party 
>A that those dastardly villains from party B couldn't possibly have 
>been taking advantage of some sneaky strategy. In the rare case that 
>you can't prove that, the aggrieved people in party A are a 
>minority, and thus unable on their own to repeal the voting system. 
>That is patently not true of Score.

I am aware of no "sneaky strategy" likely to be successful in Score. 
But, hey, I suggest Bucklin to start, and using a Score ballot to 
collect the data, with relatively low-resolution Score (like Range 4).

[...]
>What you have mentioned, as to reason 2, asserts a "disastrous" 
>impact on BR. That could certainly happen with some voting systems, 
>it's not likely with Range, and with reasonably informed voters.
>
>
>You're right; it would only be as bad as Approval, which in Warren's 
>BR simulations (with his slightly-questionable but in this case 
>unbiased-in-their-effects assumptions) is significantly worse than 
>Score or Median but still significantly better than plurality. So I 
>take back the "disastrous", where Score is concerned.

How did that feel?

>
>Basically, poorly-informed voters could indeed make serious 
>mistakes. It's natural: if a majority is uninformed, they can fail 
>to vote effectively and the loss could be serious, but not, likely, 
>maximal. (I have to except the situation where the next World 
>Dictator is on the ballot, and everyone loves him. No, I'm talking 
>about that person getting elected when a majority are opposed, 
>because they stupidly bullet vote for an array of opposing 
>candidates. That is *stupid strategy.* The amount of damage depends 
>on the method, but practically any method can be abused. Certainly Range can.
>
>
>
>In Range voting, strategic voting refers to something radically 
>different from what was strategic voting in ranked systems: in the 
>latter, it was reversal of preferences. That reversal occurs to me 
>as radically unfair, that is, a system that encourages such 
>reversals is unfair. But Approval and Range don't do that.
>
>
>Neither do most graded Bucklin methods (ie, any of them that don't 
>rely on an inherently ranked method like Condorcet for the tiebreaker).
>
>
>Right. By the way, I am *not* offended if a voting system can fail 
>in some way when faced with a tie, as long as if fails for one of 
>the two best candidates, with no major difference in utility. Voting 
>systems have various values, and simplicity is one of them, and 
>other values might suffer *a little* for simplicity.
>
>I'm proposing runoff Bucklin, and it can get a bit tricky, depending 
>on specific runoff rules. I'm suggesting reanalysis of the votes, 
>not merely picking the top two Bucklin candidates, but looking at 
>the Range winner and any candidate who beats the Range winner 
>pairwise. My suspicion is, without having done a thorough analysis, 
>that this might encourage more complete ranking (and it's for this, 
>and other benefits, that I'd turn the Bucklin ballot into a balanced 
>Range ballot).
>
>
>
>I think there are some weird circumstances with multiple majorities 
>in Bucklin that could lead a voter to think they should reverse 
>preference, but ... that is a rare circumstance, difficult to 
>anticipate, and of questionable value.
>
>
>There is no such circumstance for rational voters.
>
>
>I have none in mind. I just think I've seen some claims.
>
>
>  Obviously irrational voters could wrongly conclude this, but that 
> could happen for any method. Range, Approval, and graded Bucklin 
> methods (like GMJ) are all 100% semi-honest if voters have either 
> perfect or zero information about each ballot. (That is, if for 
> instance everyone knows that 20% of voters each are A>B, B>C, and 
> C>D, and nobody knows about the remaining 40%, then all rational 
> strategies are semi-honest)
>
>
>Basically, in Approval, a full-knowledge voter may need to cast a 
>full vote for a tied candidate, when the voter prefers another. But 
>in Approval, that's already standard strategy! In Range, that's only 
>necessary if the full 100% range vote is needed for the shift. 
>Again, it's the same, what you are calling "semi-honest." I would 
>simply say that the vote does not fully disclose all preferences.
>
>It is not "dishonest" if I don't tell you something. There is no 
>immorality in not mentioning to a buyer of some item from me that 
>I'd actually prefer to get more money for it. I approve of an offer, 
>100%, if it's what I think I can get.
>
>
>However, there are crazy circumstances of incomplete information 
>where non-semi-honest strategies are rational, for all three kinds 
>of methods. For instance, if I know that all other voters will vote 
>purely based on party, and I am the only voter who cares about 
>gender (I want to elect a woman), BUT I have no idea which party is 
>preferred by more voters, I might be rational to approve women who I 
>prefer less over men I prefer more.
>
>
>No, this is a semantic trick. If you want to vote that way, *you 
>prefer the women.* You are making a choice, based on a 
>consideration. And we call these considerations "preferences." Given 
>your *complete set of preferences*, you prefer the woman over the man.
>
>
>This is not true. I was trying to quickly state the following 
>scenario: you know that out of a million other voters, somewhere 
>from 30-70% of them will all approve both D1 and D2, and the other 
>70-30% will approve both R1 and R2. Your utilities are D1:0 D2:1 
>R1:99 R2:100. You strongly prefer R1 to D2, but because you believe 
>a D1/D2 tie or R1/R2 tie is vastly more likely than a R1/D2 tie, you 
>would rationally decide to cast the non-semi-honest ballot {D2, R2}.

Why? Why not cast (R2, R1, D2). Semi-honest. Though with those 
utilities, I think you are selling your soul for a small gain. 1 point? Why?

Jameson, there is a pathology in your thinking. You want to win, that 
is, you have a personal value for having helped to determine the 
outcome. So you will cast an approval for a candidate whom you 
essentially detest, just so that you can help this candidate to win 
over the worst D. Why? Your loss of D1 wins is very small! If, on the 
other hand, an R loses because you cast that approval, you have lost Big.

The issue here is obviously R or D. That's what your utilities say. 
If the utility for D2 were much higher, say 50, the matter might be 
different. But as you stated? No, Jameson, that's not a rational vote 
and it risks serious regret. I don't think you actually looked at the math.

I'd suggest looking at that statement about probable ties. I think it 
is self-contradictory with large numbers of votes. Are you assuming 
that all R and D voters will only vote for their own party candidate? 
You are, yourself, considering voting -- thinking it optimal -- very 
differently. If there are a million people, there will be others who 
will think like you. The vote would be dithered even if the voting 
pattern you expect is very common. And it is irrelevant, with those utilities.

The normal strategic vote in Range would be exactly your utilities, 
and I'd love to see Condorcet analysis and a runoff if needed.

>Obviously, as I went on to say, this scenario is artificial and unrealistic.

Your response is worse. That isn't sane strategy with those sincere 
utilities. Those utilities show that you only care about one of the 
Rs winning, practically nothing about which one, or if it's a 
Democrat, which one. If there were a runoff election with the two 
Democrats, you might stay home, sanely.

>In real life, you'd probably have info about whether there were more 
>R or D voters, and you'd definitely not expect to be the only one 
>with preferences among the same-party candidates. As soon as those 
>two assumptions break, this knife-edge scenario crumbles very 
>quickly. But it does in fact demonstrate a state of knowledge in 
>which a rational voter would vote non-semi honestly.

I don't see it as rational at all. And this was Approval, and you did 
not consider (R1, R2, D2). Which would be "semi-honest," stretching 
the meaning of that about as far as possible! I do *not* see that 
vote as improving your expected outcome, from the conditions given, I 
see it as worsening it.

(I'm getting that a certain approach could justify, 
game-theoretically and mathematically, adding the D2 vote. I don't 
see why you would suppress the R1 vote. How could that harm your 
outcome more than 1 point?)