[EM] Cloneproofing Random Pair and Random Candidate?

[Jameson Quinn]

2013/4/4 Abd ul-Rahman Lomax <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.


> 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.


> (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.
Many people will feel that shouldn't be rewarded, and your sarcasm isn't
going to change their mind. If that "many" is a majority, they could repeal
the system, and you'll regret that, even if you never regretted the
supposed unfairness.

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


> 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.


> this could always be alleged (providing a "whiff" of suspicion) and thus
> the best system could be shot down. Certainly Range Voting provides greater
> expected utility for a more effective vote, in terms of how preference
> strength is expressed. *However*, any "unfairness" to voters with lesser
> knowledge is simply a matter of them being politically naive. And are we
> attempting to even out the power between those who know the situation and
> those who do not? If voters don't know the situation, they probably have
> little clear knowledge of the *candidates*. A modest disempowerment of
> these people is not a bad thing. They can remedy it, easily. And if they
> don't care enough to do that, *Bayesian regret would suggest that some loss
> of effective power for their vote will improve results.*
>
> By the way, this position is not elitist. That could be me who doesn't
> understand the situation. Some people take a great interest in politics,
> others are much more passive. Neither of these is wrong or bad. Turnout
> already exerts a major push in the direction I'm talking about.
>
> However, a situation where *reversal* of a vote produces a significantly
> improved result for the voter so reversing it, represents a system failure.
> It shouldn't happen, and good systems don't encourage this. Basically, a
> naive voter can vote, in Range, just what they think, assuming that other
> voters will think like them, more or less, and the improvement by adjusting
> these voter for strategic effectiveness is small, *unless their knowledge
> level is extremely high;* otherwise there is too much noise in the system
> to truly cast a vote with serious improvement, under Range.
>
>
>  3. Strategy is a cognitive burden on voters.
>>
>
> Yes. However, for Range and Range-like methods, the burden is small,
> unless the voter wants to extract the very last iota of value out of the
> election -- in which case it can become impossible.


It's yet smaller for GMJ and SODA.


>
>
>  You seem to be saying that 1 is the only possible reason, but I weight
>> reasons 2 and 2a heavily, and 1 almost not at all.
>>
>
> Jameson, I'd ask you to consider that what I wrote was not aimed at you,
> but was a general comment about discussion of strategy in voting systems. I
> think you have missed much of my point, imagining my view to be rigid and
> narrow. I'd ask you to consider, in particular, what I wrote about the
> reception of Approval Voting, and the historical arguments about strategic
> voting there. I'm talking about something that really happened -- and that
> continues to happen.
>
> 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.


> 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}.

Obviously, as I went on to say, this scenario is artificial and
unrealistic. 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. As I said, though, you can't build such a
scenario out of a realistic model "perfect knowledge plus random noise"; it
only works with a specific (and I'd argue, unrealistic) kind of
half-knowledge.


> However, in some *other circumstance*, you might prefer the man. We vote
> based on our choices, and we make our choices, generally, based on
> circumstances. You might prefer the *individual man* over the *individual
> woman*, but you have chose to insure, as best you can, the election of a
> woman, and that's important enough to you that you would vote against the
> individual preference. This *is* a "semi-honest" strategy. It simply does
> not disclose *all* your preferences.
>
>>
>> Asset is an awesome system, but it has one flaw: it is not guaranteed to
>> resolve in any finite time. This is one of the rationales for more-complex,
>> Asset-inspired systems like SODA.
>>
>
> If it is *guaranteed* to resolve in a specific time, it will lose some of
> its power. It's a tradeoff. However, notice: we go to all this trouble to
> elect representatives for legislatures, and then they use a process to make
> actual decisions that are *not guaranteed to resolve in any finite time.*
>
> Jameson, you are raising a crazy point.


Sure, I'm not here to convince you that it's a giant flaw in asset; only
that it is a valid criticism that some people care about, and that SODA
resolves it (atmittedly at some cost in terms of Asset's other advantages).
Please do not continue to argue this point; I think we mostly agree, I was
just pointing something out.


> Asset for an Assembly election can elect, we can predict, *almost all
> seats* in very short order. Our own Asset election demonstrated the
> possibilities. It was within, I think, the same day, that I transferred
> assets to Warren to give him a Droop quota. I'd have given him more to make
> it the Hare, but we did not have clear rules. What I wanted to do was
> create a majority of the Steering Committee that, then, by unanimity, could
> resolve any other issues.
>
> An Assembly election *does not have to complete* in any particular time.
> The cost of not completing is a vacant seat and some unrepresented voters.
> Assembly rules could still count those seats in the basis for majority, so
> *there is no harm*. The loss is in deliberative representation, and that is
> a natural consequence for failure to compromise. If it's
> direct/representative asset, the electors could still actually vote, and
> they can still ask that any member of the Assembly holding a seat introduce
> motions for them.
>
> Without the Direct/Representative feature, it's a little more difficult to
> compromise, i.e., if the seat elections are totally transferring power to
> the seats, instead of just setting up access and defaults. With that,
> people with quite divergent views could still share a seat, i.e, someone
> who agrees to represent them -- but not to vote according to what they say!
> The whole point of deliberative process is to have participants who can
> change their minds, on the spot.
>
> Demoex didn't realize this, and even when it became obvious, they thought
> everyone else was wrong.
>
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