[EM] Voting by selecting a published ordering

[Abd ul-Rahman Lomax]

At 01:47 PM 5/13/2006, Steve Eppley wrote:
>Abd ul-Rahman Lomax wrote:
> > At 10:38 PM 5/12/2006, Simmons, Forest wrote:
>-snip-
> >> So most of the time, in the context of Candidate Published 
> Orderings, Concorcet will
> >> yield an unambiguous social ordering of the candidates, with no 
> cycles to resolve.
>-snip-
> >> I would say that's amazing, and extremely relevant to the topic 
> of this thread.
>-snip-
>
>I think an assumption undergirding that conclusion is questionable.

Note that Eppley is answering Simmons here, not me.

>  Given a voting method
>that tends to elect a candidate within the sincere top cycle, 
>candidates trying to win
>will tend to position themselves more closely on more issues than 
>they do under existing
>voting methods.

This is speculative, isn't it?

>   With smaller distances between candidates, other quirky effects that are
>hard to predict or analyze will become relatively stronger.

If the analysis was correct, the absolute value of the distances, I'd 
think, would not be important. Further, if we assume that candidates 
are elected based on their "positions" on issues, then, if they 
position themselves identically, *it does not matter which one is 
elected.* Of course, there are other considerations. The analysis 
presumed some kind of space occupied by candidates, with a distance 
from each candidate to another. This may have nothing to do with 
"positions" on issues. Or it may have everything to do with them.

The assumption is that preference between candidates is based on 
n-space distance. It's a loose concept, but got one better?

Simmons wrote:

>Actually, I did not assume that there was any linear or two 
>dimensional relationship. You can use any measure of closeness that 
>you want, linear, non-linear, ten dimensional, or infinite 
>dimensional (for example the norm of the difference of the quantuum 
>mechanical wave functions of the candidates, if you like).
>
>My only assumption is that there is some measure d of distance that 
>(for each pair of candidates A and B) satisfies  d(A,B)=d(B,A) , and 
>that when  d(A,B)<d(A,C), consistency requires that candidate A rank 
>candidate B ahead of candidate C .
>
>These distances are numbers, so they can be linearly ordered.

Eppley continues:

>   If candidates (and their
>supporters) do not agree on the importance of the issues--for 
>example, some may care much
>more about abortion, some may care much more about taxes, some may 
>care much more about
>health care, some may care more about corruption, etc.--then cycles 
>may not be so rare.

Justification for this claim?

>-snip--
> > I'd prefer the flexibility of Asset Voting to the fixed process 
> of Candidate Published
> > Ordering, for the latter could still create a minority winner, 
> unless the rules
> > prohibited that.
>-snip-
>
>I'm unsure what the writer meant here by "Candidate Published 
>Ordering" and by "minority
>winner."

Candidate Published Ordering is a standard fixed election method 
(assuming that the method used for counting is one that always -- 
exact ties excepted -- produces a winner. Any fixed election method, 
necessarily, can create a minority winner, which means a winner not 
approved by a majority of voters. "Approved" is a rather loose 
concept, but one measure would be that a majority of voters would 
prefer an immediate rerun of the election, with new debate and 
preferably new candidates (but including the previous 'minority' winner.)

If the voters were presented with a separate question, after the 
election, "Shall the results of the election be accepted and the 
winner take office?", a majority would vote No. That's a "minority winner."

>   When I wrote weeks ago about candidates' publishing pre-election 
> orderings, I
>didn't specify how the votes should be tallied, so in my mind we're 
>writing about a family
>of voting methods.

Technically, yes. But the method assumes that it is a ranked method. 
It *could* be IRV, but given the nature of the process, which is much 
simpler to count than standard full-Condorcet methods, because of the 
limited number of ballots in the final tallying process, there would 
seem to be no reason not to use a fully-Condorcet qualified method. 
And what Simmons claimed was that his analysis shows that cycles 
would be quite rare. If cycles are quite rare, it is reasonable to 
use Condorcet alone, with no cycle resolution process within the 
method, dealing with cycles as an election failure. Election failures 
happen even with plurality. (Things happen, such as the loss of a 
large number of ballots, the discovery of massive fraud, etc. Courts 
have been known to order elections to be held all over again.)

>   I wrote then that tallying by MAM would be good, and in some later
>messages mentioned a simple system using candidate withdrawal and 
>plurality rule.  On the
>other hand, some methods in this family would be quite poor, such as 
>tallying by Borda,
>which would encourage nomination of a farcically large number of 
>inferior clones.

Perhaps. It is not clear what would happen with Candidate-List. But 
there is no reason to use Borda.

>I don't know where the dividing line is between "rules prohibiting a 
>minority winner" and
>rules that define a member of this large family of voting methods.

Under plurality, a rule prohibiting a minority winner would be a rule 
that requires that the winner obtain a majority vote to win. It gets 
more complicated with, say, IRV or Condorcet methods, but a 
requirement might be, for example, that ballots only be analyzed, 
say, two or three candidates deep. If there is no majority winner 
with such a truncated set of ballots, then the election has failed. 
(But if there is such a majority winner, the ballot analysis would be 
continued...}

But more direct would be an Approval cutoff on the ballots, common 
with some Condorcet methods.

>Is a "minority winner" a candidate not in the sincere top cycle?

Top cycles, I think, imply that at least one, if winning, would be a 
minority winner. But the definition is not clear from a simple ranked 
ballot, there would have to be an approval cutoff.
5: A>B>C>D
4: B>C>D>A
3: C>D>A>B
3: D>A>B>C

A:B 11:4 A beats B
A:C 8:7 A beats C
A:D 5:10 D beats A
B:C 12:3 B beats C
B:D 9:6 D beats B
C:D 12:3 C beats D

If we look at these ballots truncated, assuming only the top two 
ranks are approved:
5: A > B
4: B > C
3: C > D
3: D > A

A is, of course, the plurality winner, based on first choices. A is 
the first or second choice of 8 voters, B of 9 voters, C of 7 voters, 
and D of 6 voters. Under the assumption above, A and B would be 
"majority winners," and C and D would be "minority winners."

I'm not familiar with the various methods of cycle resolution that 
have been proposed. Pure Condorcet winners have an appeal, the only 
negative aspect to them would come from the fact that the best 
candidate, theoretically, may not be on the ballot at all.

We should select executives by a search for the best, which is 
essentially a parliamentary system. And I'd prefer to move away from 
standard election methods in selecting the parliament. I'd prefer a 
proxy parliament, or the peer-parliament equivalent, Multiwinner 
(single district) Asset Voting.

>Assuming he was referring to tallying using candidate withdrawal and 
>plurality rule, I
>believe I understand his point: Some candidates might "perversely" 
>refuse to withdraw
>even though staying in elects an inferior or extremist candidate.

Under Asset Voting, candidates don't necessarily withdraw, rather 
they recast some or all of the votes they have received. They may 
distribute these votes as they choose, and I presume that there would 
be deliberative process or, what some political scientists consider a 
separate process from deliberation, bargaining.

>   Although we could
>abandon the simplicity of "withdrawal//plurality rule" for something 
>like MAM (under which
>candidates wouldn't need to withdraw to defeat inferior or extreme 
>candidates) or
>"withdrawal//Instant Runoff" (under which only some major candidates 
>would need to
>withdraw), I don't see this as a big issue.  The incentives on the 
>candidates to do the
>right thing look fairly strong.  If exceptions will be few, why 
>worry?  A legislature
>composed of a supermajority of centrists ought to perform well; a 
>few extremist
>legislators would be irrelevant.

Actually, there should be extremist legislators, as long as they are 
not incapable of participation in the process, if there are extremist voters.

>I apologize for not knowing what Asset Voting is.

It's Warren Smith's invention: 
http://www.math.temple.edu/~wds/homepage/multiwin.pdf

My own simplification I called FAAV: Fractional Approval Asset 
Voting. The ballot is a standard list of candidates, vote for one or 
as many as you like. If you vote for one, that candidate gets one 
vote. If you vote for N candidates, each gets 1/N votes.

A quota is required to win. I've assumed that a quota Q for an 
assembly intended to have at most M members would be exactly V/M, 
where V is the number of valid ballots cast, with at least one vote on them.

If a candidate receives X votes, and X = Q, then the candidate is 
elected. If X > Q, the candidate is elected, and has X - Q votes 
which can be allocated to another candidate. The redistribution of 
votes would continue until M-1 members have been elected. There are 
theoretically enough votes left to elect an Mth member, but that 
would require a consensus of those holding all remaining votes. 
Unless there is a plurality election held with those votes. There are 
other contingencies to be considered.

Bottom line, though: election failure, which in this case would mean 
the failure to elect M members (and which might be relatively 
common), can be specifically attributed to candidates holding votes 
who did not recast them.

The system could, and should, allow the election of candidates not on 
the ballot, if there are sufficient votes given to them. This would 
allow those holding votes who were unable to agree as to who to elect 
when restricted to the set of unelected candidates, to find an 
acceptable compromise.

>   I can glean something from the context,
>though.  So, let me say this: A positive aspect of the "fixed 
>process" of having
>candidates publish orderings of the candidates prior to the election 
>is that it will help
>focus attention on the candidates' and voters' relative preferences 
>regarding the various
>compromise positions on the issues.

My own view is that issues are almost irrelevant. "Almost." Issues 
serve as a way to measure candidates, but positions on issues are so 
hopelessly manufactured in order to gain votes that they become more 
of a smokescreen than real information. Asset Voting could actually 
become quite similar to Delegable Proxy simply by it becoming common 
to use write-in votes for candidates personally known to the voter.

However, back to Published Ordering and fixed process. Published 
Ordering does provide some information to the voter about the 
candidate. If a candidate publishes an ordering which displays, say, 
some party line, this is information. If a Democrat were to have as a 
second or third choice a Republican, it would show an ability to 
think and act across party lines. I personally would value that.

>   I think it's more important to elicit this info, when
>making collective decisions, than to elicit the candidates' and 
>voters' favorite
>positions.  Elections should be about making decisions in the near 
>term; there are plenty
>of other forums in which current minorities can argue that the 
>elected compromise
>positions are inferior, to try to make their preferred positions 
>popular enough to be
>adopted in the future.  If I were choosing a proxy to represent me, 
>I'd want to choose
>someone who would relatively order the plausible compromises 
>similarly to how I would,
>since ultimately one of the compromises is going to be chosen.

Personally, I'd want to choose a proxy who would order the candidates 
*better* than I could. Why not? Am I perfect in my knowledge of the 
candidates, so that someone else could not do a better job.

The *critical* action is the act of trust involved in choosing a 
proxy. Choose well

>Contrast candidates' published orderings with a more familiar 
>method, parliamentary
>proportional representation systems (PPR).  In PPR, each party or 
>candidate adopts
>positions favored by a significant segment of the voters, to win 
>some seats. (Typically a
>minority of the seats.)  After the election, the elected 
>representatives negotiate to pick
>the governing executives; assuming no faction won a majority of the 
>seats, some sort of
>compromise will be reached.  My (limited) understanding of the 
>behavior under PPR is that
>how the parties/candidates will negotiate after the election is not 
>scrutinized much
>during the period prior to the election, when the focus is more on 
>preferred positions.

This is party-system PR. Multiwinner Asset Voting can create 
non-party PR. More accurately, the voter can choose a preferred 
representative, or can choose a committee, which might all be members 
of the same party. Candidates can distribute votes within their 
party, or outside it.

The key thing about Asset Voting is that no votes are wasted unless 
there is a publicly identified person who does the wasting....