[EM] Participation

[Kevin Venzke]

Hi Abd,

--- En date de : Dim 25.4.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > I don't understand your terminology. Does "maximize
> utility" mean pick
> > the best winner every time, or does it just mean the
> method that comes
> > closest to doing this on average?
> 
> Fair enough, I'll need to express some definitions, and I'm
> going to keep it simple, and define a UM criterion,
> Utility-Maximizing. The UM ballot allows the expression, for
> each candidate, of some fraction of a full vote, i.e., each
> candidate receives a vote in the range of 0-1 vote. A
> "sincere UM ballot" is one in which every preference
> expressed is real, i.e., if the vote for one candidate is
> greater than a vote for a second candidate, then the voter
> actually prefers the first candidate to the second. However,
> the reverse is not necessarily true. If a voter prefers a
> candidate to another, it is possible that the voter chooses
> to vote the same fraction for them. I will assume, however,
> that the ballot allows the voter to express all preferences
> if the voter so chooses. (So it is, at a minimum, a Borda
> ballot).
> 
> A "UM ballot equivalent" is a ballot from another system
> translated to a UM ballot without violating the assumptions
> of the UM ballot and without creating discriminatory
> information not present on the other system's ballot.
> Example would be:
> 
> Plurality: One candidate, 1 full vote, all other candidates
> 0 vote.
> Borda: For N candidates, ranked, a vote of 0 for the lowest
> ranked candidate, 1 for the highest, and fractions of 1(N-1)
> stepwise for each in order of preference. (Unaddressed: what
> if the voter does not rank all candidates?)
> Range is a UM ballot intrinsically. (This includes
> Approval)
> Ranked methods without approval cutoff: Borda equivalent.
> Ranked methods with approval cutoff: ranks assigned are
> distributed equally across the range of 1/2 vote to 1 full
> vote for candidates approved, and across the range of 0 to
> 1/2 vote for candidates disapproved, but not 1/2 vote.
> (i.e., if there are two disapproved candidates, and if a
> preference is expressed, the most disapproved would be
> assigned 0 vote and the preferred one would be assigned 1/4
> vote. If three, the votes assigned would be 0, 1/6, 2/6,
> etc. (unranked candidates are assigned 0 vote, note that
> this, however, is "equal ranking." Which is frequently
> allowed in methods that supposedly don't allow equal
> ranking.)
> 
> A voting system satisfies the UM Criterion if it never
> chooses a candidate with a sum of votes on a UM ballot
> equivalent to the ballot used by the voting system, who has
> a lower sum of votes than the maximum among the candidates.
> 
> Plurality satisfies the UM Criterion because it does not
> allow the expression of other preferences, and, note, it
> must be this way because Range can be voted this way, if the
> voter has a preferred candidate. I.e., the equivalent of a
> Plurality ballot can be cast in Range, and if all voters do
> this, Range will provide a Plurality result.
> 
> >  Either way isn't it just *one* method?
> > I could believe that that method doesn't satisfy
> LNHarm, but it would be
> > hard to demonstrate that that method was the big
> winner.
> 
> "Method" the "big winner"? For the Later No Harm thing,
> it's quite enough that no ranked method satisfying Later No
> Harm -- which only applies to ranked methods or other
> methods allowing voting for multiple candidates while
> expressing a favorite -- cannot satisfy the Condorcet
> Criterion, not to mention the UM Criterion.

What do you say about the fact that Condorcet is almost certainly not
compatible with "UMC"? The CW has an above-average Borda score but of
course not always the highest. (At least, that is true with complete
rankings.)

Also, since the UM Criterion is based on positional assumptions
(when applied to a rank ballot) rather than actual utility, it's 
unclear that the best method possible (in terms of utility) satisfies 
UMC.

> > > And no method that maximizes social utility,
> overall
> > > satisfaction, can satisfy the majority or
> condorcet
> > > criteria, as fundamental as they seem, when only
> a single
> > > ballot is used. They can by using a second ballot
> to ratify
> > > (or reverse) an original election that finds the
> utility
> > > maximizer.
> > 
> > When we analyze methods we will usually assume that
> voters don't change
> > their positions between rounds, and the same voters
> vote in both rounds.
> 
> Which was, certainly, a simplifying assumption which
> completely neglects the reality of voting in multiple
> ballots.
> 
> (1) It's a different set of voters, usually.
> (2) They change their minds, based either on the first
> results, or on new information, or both.
> 
> By making this assumption, the analyst is tossing aside the
> reasons given in Robert's Rules of Order for holding
> repeated balloting instead of election by plurality or
> deterministic preferential voting.

However, we need to be able to say *something* about the situation in
subsequent rounds, in order to define any criteria.

> > It's hard for me to imagine what approach could be
> used to show the
> > utility advantage of multiple rounds.
> 
> It's obvious, actually, but it depends on the polling
> method used. Note that Range voting, Warren Smith showed,
> isn't ideal because of normalization error, assuming that
> voters normalize to a full power vote, and that Range with
> top two runoff actually had superior performance. That's
> because, I assume, voters renormalized to the candidate
> set.

This finding by Warren surprises me greatly. If you get a better result
from renormalizing for a specific pair of candidates, wouldn't one
expect this means we should be doing that all the time instead of dumping
everyone into the same pot? Why on earth doesn't normalization mess
things up there?

Additionally isn't the main idea for Range that sometimes the majority is
wrong? Surely Warren's finding doesn't include the notion that voters
could change their mind in the second round.

> > > Not necessarily. Suppose I have a favorite I rate
> at 10.
> > > But there is another candidate who is really
> almost as good,
> > > and, in fact, this candidate I rate at 9 is
> better than I've
> > > every experienced being elected. Am I harmed if
> my lower
> > > ranked vote for the 9 causes the election to
> complete for
> > > this candidate, whereas without my vote perhaps
> it was a tie
> > > and it went to a runoff between the 9 and the 10?
> And did my
> > > adding that other vote actually "harm" my
> candidate, or did
> > > it merely reduce my support for the candidate?
> > 
> > Unless you want to invent new terminology, then yes,
> you are "harmed"
> > when your 9 vote moves the win from the 10 candidate
> to the 9 candidate.
> > I don't know what the practical difference is between
> "harming" your
> > 10 candidate and "reducing your support thereby making
> him lose."
> 
> Absolutely, this is the way "harm" is used. However,
> socially, it's bogus. I have a value to finding a
> compromise, and, in real election terms, I'd be thrilled to
> see my 9 elected!
> 
> I didn't make him lose, I, in fact, gave him support toward
> winning. Just not maximum support, focused between him and
> the 9. Pure ranked methods allow me to exert maximum vote
> strength between all pairs of candidates, typically, as if
> my utility difference was maximum, full strength, between
> all pairs. What Range does is to require me to limit my
> voting power to a *sum of vote strengths* equal to one
> vote.
> 
> No, I didn't make him lose, the rest of the voters did! I
> voted to prefer my favorite and, in Range, gave him a tenth
> of a vote over his nearest competitor.

Well, we say you "made him lose" because if you did that one thing
differently it wouldn't have happened.

> > The reason we expect that to be bad is that if next
> time you choose
> > not to rank the 9 candidate, you could let your 0
> candidate win, which
> > isn't what we want because we (the scenario designers)
> know that you
> > actually did have a compromise choice.
> 
> Who should have the choice, voting system designers or
> voters? 

Of course the belief is that voters would not want to have to make this
choice at all. (And all things being equal, I think that's fair. We
don't usually assume the voter has a "treat my vote completely 
differently from this" option.)

> > > The goal of voting systems is to find a social
> compromise,
> > > and to fulfill that goal the favorites of many
> voters,
> > > sometimes even a majority of voters, must be
> "harmed," if we
> > > think not being elected is a harm.... Compromise
> is
> > > essential to community decision-making, and it
> always
> > > involves this kind of "harm." What a
> Later-No-Harm method
> > > does is to protect the voter from "harming" a
> candidate by
> > > taking the candidate out in back and shooting
> him. And then
> > > the method comes back to the voter and says, "Now
> that it
> > > won't harm your candidate, may he rest in peace,
> who else
> > > would you like to vote for?"
> > 
> > That's IRV.
> 
> You got it.
> 
> >  Most of the LNHarm methods don't eliminate
> candidates, the
> > particularly interesting ones being DSC and MMPO. (DSC
> gradually "rules
> > out" candidates but this isn't a prerequisite for
> counting lower prefs.)
> 
> Well, I'd like to see it. If I reveal some preference for a
> lower ranked candidate, at all, I don't see how this could
> never "harm" my favorite under all conditions.... But I
> suppose there are lots of things that exist that I don't
> see.

Ok. DSC is a little difficult to explain so I will describe it for
the three-candidate scenario. It's a rank ballot. You can truncate but
normally equal rankings are not imagined (the method as designed wouldn't
reward it anyway).

We find six scores: The first preference count of the three candidates,
which I'll name {A} {B} and {C}; then we also find the strict last
preference count of the three candidates, which I will call {BC} {AC}
and {AB} respectively.

Sort the six in descending order. Then go through the sorted list one
by one. Label as "disqualified" every candidate not named in the braces,
unless that would leave as disqualified all candidates. When only one
candidate is not labeled "disqualified" then he wins.

So when you add a preference, changing an A ballot to an A>B ballot,
the effect of this is to harm C (perhaps to elect A or B instead). But
it can't move the win from A to B because A was not directly hurt and
B was not directly helped.

Example:
40 A>B
25 B>C
35 C>B

The sets are {BC} 60, {A} 40, {AB} 40, {C} 35, {B} 25, {AC} 0.
The {BC} 60 disqualifies A. {A} 40 is ignored because we can't disqualify
everyone. {AB} disqualifies C. So B wins. (The two 40's could be taken
in either order with the same result.)

Point to notice is that IRV would eliminate B, and the 40 A>B voters
would be unable to "transfer" their preferences in any sense.

MMPO uses a similar principle: We elect the candidate who has the fewest
votes against him in his worst pairwise contest. It doesn't matter
whether he wins that contest or not. (This has some negative consequences
unfortunately.)

So the effect of adding a preference is to hurt inferior candidates,
without altering the relationship between a higher preference and the
newly added preference.

Another simple example would be Antiplurality on rank ballots.

> > > However, sauce for the good is
> > > sauce for the gander. If the method hadn't taken
> my favorite
> > > out back, if my favorite remained in the race,
> the method
> > > can still come to me and say, "is there anyone
> else
> > > acceptable to you?" And while my answer might
> "hurt" my
> > > favorite, on the other hand, the answers of
> others might
> > > "help" my favorite. My answer only has the
> possibility of
> > > "hurting" if my candidate wasn't going to win
> without
> > > additional votes.
> > 
> > However, if my answer might harm my favorite, and I
> think other voters
> > may help my favorite, then I could conclude that I
> shouldn't risk harming
> > him.
> 
> You could. Wouldn't it depend on the severity of the risked
> harm? 

Yes.

> This is why thinking in terms of "harm" to candidates
> instead of to voters misleads us. If my real utilities are
> 1.0 and 0.9 (and these mean low preference, quite low, I
> rarely see such low preference in real elections, at the
> high end), my "candidate" might be "harmed" (and in systems
> where a candidate has to seriously bust himself or herself
> to get elected, it can sure seem that way), but the harm to
> me is small, and my own voting is based on my own sense of
> harm. I very much doubt that I would ever regret voting 1.0,
> 0.9, from seeing the 0.9 be elected.

Ok, but at some point doesn't it start to matter? What if it's 1.0 and
0.7?

> > > >  He could (depending on many factors,
> reasonably
> > > or
> > > > unreasonably) withhold lower preferences as
> a result,
> > > which means less
> > > > sincere voting.
> > >
> > > No. This is a very common error. One withholds
> lower
> > > preferences because the preference strength is
> high.
> > 
> > Well, I hardly think that can be said as a general
> rule without regard
> > to what election method is being discussed. Personally
> where I withhold
> > preferences in Bucklin is not going to be the same as
> where I withhold
> > preferences in IRV.
> 
> IRV is a completely bizarre system. In Bucklin, you will do
> as I mentioned, and we were talking about systems that break
> LNH, and especially about Bucklin.

Bad example then. Where I would truncate under Schulze is not the same
as where I would truncate under Bucklin.

> > > Truncation is not insincere, quite likely. A good
> voting
> > > system solicits and rewards sincere votes, and
> what we have
> > > done is to assume that voters aren't sincere when
> they say,
> > > "I prefer my favorite enough that I don't want to
> take a
> > > chance of electing someone else, I'm willing to
> take the
> > > risk that my vote becomes moot."
> > 
> > That's not an assumption, that's a definition. If
> you're not listing
> > lower preferences because you *perceive a risk* to
> doing so, that is what
> > we usually consider "not sincere."
> 
> And that is a definition that was invented in order to
> define Approval as violating certain criteria. Not sincere
> used to mean "reversed in preference." 

I think that is an odd analysis but anyway you seem to backtrack:

> I probably expressed
> the thinking of the general truncating voter poorly. Put it
> this way: "I prefer my favorite, and I don't give a fig
> about the remaining candidates, or I'm not going to bother
> to try to figure out which ones I might prefer." Is that
> sincere?

Much more likely, in my opinion.

> > > >  Usually sincere voting produces a
> better
> > > outcome, in
> > > > this case due to a greater amount of
> information
> > > provided. So ultimately
> > > > the good of the electorate is the
> consideration.
> > >
> > > "Sincere voting" is unfortunately not well
> defined, and so
> > > the statement that "sincere voting" is better is
> > > problematic. I agree that more information is
> better, but
> > > what kind of information? If incommensurable
> statistics are
> > > amalgamated, the result is noisy.
> > 
> > That's something to debate, but the only point I was
> making is that
> > LNHarm and other criteria are philosophically aimed at
> the good of the
> > electorate.
> 
> LNH isn't, for sure, because the candidate who maximizes
> the good of the electorate can be excluded because of it.

??? I said they're "philosophically aimed." You can disagree that they
accomplish what they aim to do but it is still the aim.

> >  All things being equal "sincere" is better than
> "insincere."
> > Maybe there is some incompatible type of voting that
> is better than
> > "sincere," but then all things aren't equal.
> 
> LNH generally involves nondisclosure to the voting system.
> The information may be on the ballot, but it isn't disclosed
> until the favorite is eliminated. Now, you've said something
> different that's news to me, that some methods satisfy LNH
> but also disclose the "later" preferences. I don't
> understand how that trick is pulled off.

Well, it's certainly true that there is some concealing of information.
The debatable point is whether this can be worthwhile anyway.

> > I don't really understand how the runoff finalists are
> selected. Are
> > you going to let a faction tie two clones in first
> place and have them
> > both go to the runoff?
> 
> Well, show me a scenario and I'll see. Here is how I'd
> choose runoff candidates. The condition is that no candidate
> gains a majority. Clones, generally, would be roughly tied,
> because it's likely that they'd have additional votes from
> the supporters of each other.
> 
> I'd look at, however, at the Bucklin winner, i.e., the
> most-approved candidate. I'd look at the ballots to see if
> there is a Condorcet winner. And I'd look at them to see if
> there is a Range winner, i.e,. the ballots counted as Range
> ballots. That gives me up to three candidates. Often,
> though, some of these kinds of winners will be the same
> person. So we might have one or two candidates. If we have
> three or two, those go to the runoff. If there is only one,
> good chance this is the best winner, but to be sure, because
> we don't have a majority, we should pick another.
> 
> How? The scenario proposed, that has two clones tied for
> first place, would be political suicide for that faction,
> generally, because much of an election is campaigning and
> name recognition, dividing that between two candidates is
> likely to damage both of them, that they got to first place
> is pretty significant; i.e., it probably means that one of
> them would have done even better if the faction had been
> united.

I don't think so: If getting your supporters to rank two candidates
equally high is a viable strategy to winning without having a (meaningful)
runoff, I think parties will regularly run dummy candidates alongside the
serious candidate even though that means the second round of voting will
be basically pointless.

I don't think even independent-minded voters would fix this. If parties
are setting it up so that you have a single-ballot plan for autowinning,
independent-minded voters will see it as just as valuable as anyone
else, unless they actually desire to see a runoff (which would be kind
of hard to explain in terms of utility).

Kevin Venzke