[EM] Participation

[Abd ul-Rahman Lomax]

At 01:24 PM 4/25/2010, Kevin Venzke wrote:
>Hi Abd,
>
>--- En date de : Dim 25.4.10, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> a écrit :
> > That's right. But until utility analysis started to be
> > done, the arguments had practically no foundation, they were
> > just ideas about what democracy should look like, sometimes
> > intuitions, and sometimes quite deceptive. Some criteria may
> > be positively harmful, and Later No Harm is one of those. No
> > method that maximizes utility can satisfy Later No Harm, no
> > method that finds the best compromise winner can satisfy
> > it.
>
>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.

> > 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.

>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.

And that's only the start of it. Voter turnout 
depends on preference strength over the candidate 
set, so turnout modifies even Range votes to 
express those with higher preference strength, 
and I doubt that Warren simulated this. It's 
highly likely that differential turnout in runoff 
voting shifts results toward what would have been 
the Range winner with sincere ballots in the primary.


> > 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.

>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? Yes, I could choose not to 
rank the 9 candidate, but get sensible! My 
preference strength between that candidate and 
the 10 is practically nil. (I'm sort of amazed at 
voting scenarios, I've seen at FairVote, where 
many voters prefer A to B, 100 to 99 rating. And 
then along comes somebody who thinks very 
differently and rates A 0 and B 100, and B wins 
the election and supposedly the A voters are 
Shocked! Shocked! How could such a massively preferred favorite lose?

But in fact, A was not "massively preferred," but 
was "maximally weakly preferred," within the 
Range 100 system in which those voters were 
voting. If they voted that way, they were saying, 
in effect, "It's really no big deal to use which 
is elected, A or B, so we will leave the election to people who care more."

And that is how people really make decisions in functional societies.

>I guess your response would be "maybe the 9 candidate sucked." Maybe,
>but we don't know, and I tend to think that in general, compromise
>choices provide better utility than flank candidates.

Sure. If we assume that left and right candidates 
are on some issue scale, and that voters have 
positions on that scale, and that relative 
utility for two candidates has to do with 
relative distance from the voter to each 
candidate, then a candidate near the median 
position will very likely maximize overall 
utility. But, of course, it's not always that simple.

A lot of study of "strategic voting" in Range has 
been mangled through the assumption of 
contradictory conditions: i.e., a voter 
supposedly has little difference in utility 
between two candidates, but "exaggerates" by 
expanding the Range distance between them. I.e, 
supposedly the voter would "sincerely" rate one 
candidate at 10, and another at 9, but instead votes 10 and 0.

What I wonder in a situation like this is why the 
voter bothers voting at all! If the voter 
believes that the only realistic possibilities 
are the 10 or the 9, then *of course* the voter 
will normalize to the realistic candidate set. 
Tell me, which would you prefer, and how 
strongly, $1000 or $900? If you knew that the 
only likely choices were those two, would you, in 
a vote, put 1 vote on the $1000 and 0.9 vote on the $900?

Only if there were, say, three realistic choices, 
and you have zero knowledge as to which one may 
prevail, would you vote 1.0 and 0.9.

But both votes are sincere, since preference has 
not been reversed. Only with a new and not really 
well-defined meaning for "sincere vote" was it 
possible to assert that they were insincere.

(And, then, suppose that the two most likely 
outcomes, by far, are the $900 and $0. Would you 
vote, then, $1000 and $900. Maybe. More likely, 
you'd be thrilled to get the $900 so you would vote 1.0, 1.0.)


> > 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.


> > 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? 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.

> > >  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.


> > 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 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?

>There could certainly be *useful information* in where people
>strategically truncate, but that doesn't mean we call it "sincere."

Sincere to means "expressing a sincere preference 
between sets." Lumping together candidates in the 
presence of *some* preference is not insincere. 
Sometimes people talk about "fully sincere," 
meaning that every preference is disclosed, no 
matter how small, but this leads to some 
preposterous assumptions; it's assumed, 
typically, that voters always have a preference. 
In fact, we don't. Or perhaps we have a 
preference but it is so small that it's very 
noisy, it changes from day to day, and if you 
were to ask us how much we'd spend if we could be 
assured of the election of two such candidates, 
we'd come up with the same amount. (Or to be 
assured that they would both lose, if our 
"preference" is negative for both of them.)

> > >  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.

>  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.


> > I've been working pretty intensively on Bucklin, and I
> > believe that a strategically optimal Bucklin ballot, if
> > Bucklin is used in a primary -- I'm leaving aside for the
> > moment of Bucklin used as a deterministic runoff -- is a
> > Range 4 ballot with sincere ratings based on the favorite
> > being a 4 and all candidates preferred to a runoff being
> > rated 2 or 3. This has to be Bucklin-ER, of course. It gives
> > the voter no strategic advantage to vote this ballot
> > insincerely. If they prefer the runoff to every candidate
> > other than their favorite, *they prefer the runoff*, and
> > they might truncate entirely. It's a sincere vote, and it is
> > on a scale that treats all voters the same, assuming that it
> > is equally valuable to them to avoid a runoff, as an
> > absolute.
>
>What we would do there is analyze it as a ballot with an explicit
>approval cutoff.

Yes. That's what I'm doing. On a Bucklin ballot, 
all votes are "approved" votes, if there is a 
runoff. It means "approved compared to not 
completing the election." It means "I'm willing 
to cause the election to terminate with this candidate."

>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.

We've just defined that the Bucklin winner and 
the Range winner are the same. Is there a 
candidate who beats the Bucklin/Range winner? If 
so, we've defined that this is not a Condorcet 
winner, is there a cycle? What other candidates 
might the electorate actually prefer. I very much 
dislike leaving out of a runoff a candidate who, 
on the face, would beat a candidate who is going 
to the runoff. But I'm not going to exhaustively define this now.

>Are your ideas on this at the bottom of this post?

Yeah, I did say it. The Bucklin winner is an 
"Approval winner" with an approval cutoff lowered to a certain point.

> > I believe that this method will discover if a majority of
> > voters are ready to settle on a candidate. If they aren't,
> > it will give them very good information to use in
> > determining how to vote in a runoff.
>
>But just like with TTR, the fact that there is a second round provides
>incentive to *not* find a majority in the first round. That's not
>necessarily bad though.

It all depends on preference strength. The 
incentive, in fact, encourages more accurate 
voting for the approved set. And if there is an 
additional "disapproved" rank, i.e, rating 1 
added to the scale I described, and if this would 
help a "better disapproved candidate" to get to 
the runoff, making it more likely that the runoff 
could be more pleasing in outcome to me, then I 
have a motive to add that rating. It's not going 
to cause my favorite to lose, and it can't cause 
that candidate to win the first round, it isn't 
used for that. It's only used to (1) provide a 
better picture of how the electorate views all 
the candidates, which is helpful for future 
elections, and (2) possibly make better choices 
for runoff candidates, indicating one or more of 
them who aren't "quite so bad."


> > As a ranked ballot with
> > four ranks (including the bottom), Condorcet analysis can be
> > done, whether it is used for the election or not. I've
> > suggested adding an additional rank, rating value 1, to be
> > used to make the scale symmetrical, these are not approvals
> > of the candidate, but they can be used to estimate overall
> > utility.
> >
> > To me, it's quite important to start collecting much better
> > ballot data, and this would do it, with sincere votes
> > incentivized. The ratings of 1 would not harm any approved
> > candidate, they merely would be a way for voters to make a
> > discrimination between the unapproved candidates. They could
> > be used to determine runoff candidates (and with a good
> > runoff method, it's possible for there to be more than two
> > runoff candidates, such as the Approval Winner, the Range
> > Winner, and a Condorcet winner, if they differ (which would
> > be rare)

I'm not settled on what the optimal runoff 
candidate set would be. If the runoff method is 
Bucklin again, there can be more than two without 
harm. But this time voters will know that it's 
their last chance. They can't put off lower rated 
approvals again. However, helping them greatly, 
they will have the results of the first election, 
they will all, if they want to be, accurately 
informed about how the rest of the electorate 
feels about all the candidates remaining on the 
ballot. They will know the risks of continuing to 
bullet vote, and they will make their choice.