[EM] Approval reducing to Plurality

Abd ul-Rahman Lomax abd at lomaxdesign.com
Wed Sep 1 08:19:37 PDT 2010

At 03:02 AM 9/1/2010, Kristofer Munsterhjelm wrote:
>robert bristow-johnson wrote:
>>On Aug 31, 2010, at 4:03 PM, Raph Frank wrote:
>>>On Tue, Aug 31, 2010 at 11:08 AM, Juho <juho4880 at yahoo.co.uk> wrote:
>>>>The serious problems of Approval come into play only when there are more
>>>>than two potential winners. As long as T1 and T2 are called "T" (i.e.
>>>>"minor") things are fine.
>>>I disagree.  However, we don't really know the how the mechanics of
>>>approval will work out in practice.

Well, that's not entirely true. Approval Voting was used for hundreds 
of years in Venice. Further, Bucklin is a form of Approval Voting, 
and was rather widely used for up to a decade or more in the U.S. 
I've seen Approval Voting in practice in a small organization. It 
works when there are *many* candidates.

A common error on this list is to only think of election methods 
within a narrow context: deterministic public elections. The majority 
of elections held are not such elections.

Top-two runoff is almost completely neglected here, though it is the 
most commonly implemented election reform. It's not deterministic 
from a single ballot. People often analyze it as if it were a single 
election, i.e., they assume that it is simply a drawn-out IRV 
election. It isn't.

And these assumptions work against considering Approval in the best 
context: as a primary round in a runoff system. Don't just assume it 
would be top-two runoff, and don't assume that if there are multiple 
majorities, the one with the most votes wins! That's a good rule for 
a single-round deterministic system, but is not necessarily optimal.

Rather, I've been suggesting, use Bucklin as a primary method in a 
runoff voting context, and hold a runoff if there is no majority 
winner, and *possibly* include as a situation requiring a runoff that 
there are multiple majorities.

Further, use a range ballot for the Bucklin election, where the 
ballot has an explicit approval cutoff, and do various forms of 
analysis on the ballots; in particular, check for a Condorcet winner. 
A Condorcet winner must be in the runoff. Check for an Approval 
winner. An approval winner must be in the runoff. Check for a Range 
winner. A range winner (with default zero rating if not rated) must 
be in the runoff. Check for a Bucklin winner (this is a generalized 
Bucklin run by sliding down the Range scale, seeing a majority.)

And the runoff is Bucklin as well, and write-in votes are allowed. 
Now, what is the optimal winner of the runoff? To really determine 
that, we should have (1) real ballot data to analyze, and (2) good 
Bayesian regret simulations to optimize real SU, based on expected 
strategies of voters. But I'd start with Bucklin. The runoff might 
not be a Range ballot, but a simple Bucklin one, three-rank, with the 
default disapproved rank for blanks.

There is no truly satisfactory single-ballot system; the basic 
problem is that voters typically don't have enough information. The 
only exception I'd propose is not actually a single-ballot system, 
Asset Voting. It is, rather, an organizational trick, reducing an 
election decision to a deliberative process involving a greatly 
reduced set of participants.

>>>I think that it would allow a little utility weighting to come into
>>>it.  Voters who see two candidates as being almost identical would
>>>probably just approve both.
>>i can confess that i am currently planning to bullet two (out of 
>>about 20, with limit 6) candidates this November in this virtual 
>>approval election of state senators.  the candidates are clearly 
>>different, but i like them both.  neither are incumbent.  there are 
>>two "open" seats and 3 credible non-incumbents to fill them.  so 
>>it's kinda like musical chairs.
>>and my worry is that voting for one will harm the other.
>Vote for both of them. In the worst case that they cancel out, it'll 
>be the same as if you didn't vote for either, except that you've 
>increased the chance that the winners will include at least one of them.

That's correct. First of all, don't think of "harming" candidates. 
Vote to "help" candidates. With Approval voting, your votes are truly 
independent. You could "help" all candidates (vote for everyone!) or 
none (vote for none, or for a useless name). If one of the candidates 
you favor would win without your vote, the candidate will win with 
your vote. Unless you vote for someone else! If you vote for two 
approved candidates, your vote will not change the choice between the 
two. This concept of "harming candidates" comes from the rhetoric of 
instant runoff voting, where, in order to keep you from "harming" 
your favorite, they take the favorite out back and eliminate him. 
That way, you can't harm him! Now, if you could choose how your vote 
would be counted, would you, to keep from "harming your favorite," 
eliminate him?

Basically, supporting instant runoff voting is making that choice. 
Instead, better systems, like Bucklin, leave your favorite in play. 
If you vote for someone else in the next round, you have, just for 
the pairwise contest between the two, stepped out and have abstained. 
You have not "harmed" your favorite, except in the sense of not 
maintaining an exclusive preference. But in a hybrid system, you can 
have your preference cake and eat the benefits of compromise as well. 
I.e., you might help someone other than your favorite make it into a 
runoff. Is that "harm"? I'd call it working to help the society make 
a better choice! Surely that helps everyone who is concerned about 
social unity and welfare!

But even if that other candidate "wins" the first round (in a runoff 
election) Bucklin count, say, your expressed preference could cause 
your favorite to "win" the Condorcet comparison. Your ratings might 
help your favorite win the Range comparison. And so both would get 
into the runoff.

And then you would very likely have some accurate data on which to 
refine your choices in the runoff.

And if you don't care? What if your two favorites make it into the 
runoff, and nobody else, and there is no viable write-in candidacy?

Whether or not you bother voting depends on how much you are. In a 
runoff election, there is a genuine test of sincere preference 
strength. The idea that absolute social utility is not usable in 
voting systems is a myth. It shows up, even without complex systems 
like a Clarke tax, in voter turnout. Runoff elections tend to have 
low turnout *because voters have less concern about the outcome!*

(Sometimes turnout is higher in a primary for a different reason. 
Elections have been combined, and the election in question is being 
held as part of a general election with other issues considered more 
important. This is an inflated turnout, and introduces noise into the 
system, almost as badly as mandatory voting. It increases the power 
of media, able to amplify votes through name recognition, encouraging 
people to vote vague impressions, which can be skillfully manipulated 
by experts at such. This is the primary way that money influences elections.)

>>>It is like condorcet with a slight utility bias.
>>what's the utility?  that it's easy to understand?  or something else?
>It's utility as in utilitarianism. Abd likes to use the example of a 
>pizza, where a majority likes one type of topping slightly more than 
>another, but there's a small minority who absolutely detests the 
>first type. Then, it is argued, the good thing is to pick the second 
>topping because the majority loses less than the minority gains, 
>even though that violates the principle of majority rule.

And I'm also making the point that this is how people really make 
decisions in small groups. It does not violate majority rule *if the 
majority accepts the result.* And that is what really happens in 
small-group decision-making, even when the process is formal. 
Standard process does it through single-issue (Yes/No) voting, 
iterated until there is a majority. Range data, effectively (but 
informally) is incorporated in the deliberative process, and in the 
fact that in standard process, a final, decisive vote is not held 
until a two-thirds majority decides it is ready to vote.

I've encouraged looking at election methods within the overall 
context of collective decision-making. In that context, we can 
readily recognize a fear of "harming one's favorite" as a fear of not 
getting what one wants the most, but instead getting an acceptable 
compromise. In other words, succumbing to this fear is simply being 
selfish, bluntly put.

I want my Pepperoni pizza, and I don't care if my "friend" will break 
out in hives. Let me go without, it won't kill him. And my Jewish 
"friend"? Why does he have such a silly religion, anyway, that 
prevents him from eating the most wonderful pizza in the world, Pepperoni.

>In that sense, Range has a utility bias - it picks winners based on 
>(reported) utility rather than on the number of voters who state the 
>preference. The problem is that reported utility can easily be 
>falsified, and so Range reduces to Approval.

I've done a lot of analysis to show that there is a logical error 
here. "Falsified" implies that there is some "real" vote that is 
different from how the voter votes, and not simply different in being 
more accurate than the actual vote (i.e., the actual vote is "rounded 
off") but "exaggerated." Why? Why would a voter "exaggerate"? There 
is a basic error here, in understanding how people make decisions. We 
make decisions based, not on absolute utilities (which would be "real 
utilities," I'd suspect), but on relative ones, modified according to 
our assessment of what is realistic as a choice. So, say, a Christian 
might really prefer The Messiah, greatly, over a candidate on the 
ballot. So, if it's a Range ballot, does the voter accurately 
represent (as a write in) The Messiah as 100, and the otherwise 
favorite as 1? Or 10?

No, the voter votes von Neumann- Morganstern utilities, which are 
normalized absolute utilities adjusted for expected effectiveness. We 
don't want to waste our vote!

Voters will do this: They will consider, not all candidates, but all 
realistic candidates. They will then optimize their vote over that 
set. If the system allows them, they will express "moot preferences," 
i.e., a preference for a minor candidate with no chance of winning, 
but they will prefer, usually, to minimize the voting power they 
spend on that. Good systems will allow them to express a minor 
preference without wasting their vote. (IRV does, in theory, do this, 
but it also introduces some awful pathologies. Decent Bucklin systems 
allow this practically without restriction).

>  CWP is probably better than raw Range at forcing the voter to be 
> consistent, but in so doing, it fails many properties that Range 
> advocates consider important, like the utility bias above - since 
> the direction of the pairwise victories are determined by ranking, 
> a method based on CWP passes Majority even in the pizza example above.

Majority is essentially a defective criterion, like the Condorcet 
criterion. These criteria are useful; in my view, when a Condorcet 
winner, for example, as shown by ballot analysis, fails to win a 
Range election, the electorate was actually not ready to make a final 
decision. There should be a runoff.

It is possible, I believe, to set up a runoff voting system that will:

1. Minimize runoffs, by finding majority winners more efficiently in 
a first round than either Vote-for-One or even IRV (which usually 
fails to find a true majority if it would not have been found with 
Plurality). (IRV proponents argue that it finds majority winners, but 
it easily and frequently finds a winner who was opposed by a majority 
of voters. And it can pass over a candidate who was preferred by a 
majority of voters -- it is simply that this candidate did not have 
enough 'first preference' votes.)

2. Always produce a true majority-approved result, except in 
extremely rare situations (where it has been determined that a result 
*must* be found by the second ballot, in which case it can be a 
plurality-approved win.)

3. Identify sincere range (utility) winners and give them a serious 
opportunity to win majority -- or at least plurality -- approval.

4. Be precinct summable. Complex analysis, which might be needed with 
certain close elections, need not be done immediately. (This complex 
analysis would be Condorcet, which is still precinct-summable.)

5. Be easy to vote.

What should communities do? They should establish a study committee 
to gather information and analysis on voting systems. The committee 
should then make a report that attempts to be complete and unbiased. 
Minority reports should be issued. Public comment should have been 
solicited as part of this committee process. Then, when a draft 
report is prepared, there should be additional public comment, before 
a final report is prepared. That's a final report of just the first session!

Voting systems are very important, they determine the process by 
which we make decisions, either directly, as in elections and ballot 
questions, or indirectly, even more importantly, as in determining 
the composition of legislative bodies, which then make decisions on 
behalf of the general public. It's worth taking the time to do it right!

But the process does not end there. The study committee would, in its 
report, recommend one or more possible voting systems for local 
trial. Cost estimates should be prepared. There are some voting 
reforms that are practically no-cost, and that do no identifiable harm.

Approval Voting is one of these. The bugaboo raised about AV is that 
the majority criterion will be violated through the appearance of 
multiple majorities. This is actually extremely unlikely. Rare upon 
rare, and if it does happen, the community should be grateful, for it 
is lucky to have so many qualified and widely acceptable candidates! 
No, far more likely is that no majority is found. Bucklin does 
better, by allowing ranked approvals.

Bucklin requires some spending on a more complex ballot, but is still 
countable with classic voting machines and technologies, unlike IRV.

A study committee should be rather insensitive to arguments about 
"momentum," which is pretty much the standard fall-back argument of 
FairVote for IRV. It's a lousy method, but ... hey, it's better than 
Plurality and only you election methods ivory-tower fanatics think 
anything else has a chance ... so why don't you support it? After all 
it is better than PLURALITY. Ever hear of Bush v. Gore? Huh? Answer 
me that! Did I mention that it's better than Plurality?

Learning something about the history of voting systems could be very 
useful. FairVote has presented the history of Bucklin in the U.S. in 
a highly distorted way. The fact is that Bucklin was dropped for two 
basic reasons: first, it produced results that the political 
oligarchy didn't like. I.e., it worked. And second, it was, just like 
IRV more recently, was sold as a method of finding majorities in a 
single round.

As people became more sophisticated voters, Bucklin may have tend to 
do that less often. (In some of the early Bucklin elections, there 
were, in fact, multiple majorities found.) Plus, in some elections, 
the electorate simply is not ready to make a decision with a single ballot.

(Runoff voting is not merely a method of picking a winner, it is a 
method of focusing attention on the most likely winners. I.e., it 
makes better decisions, better than you could imagine just by 
thinking about it as a pure ballot, instant-decision, method. One of 
the stupidest applications of IRV would be in a direct, deliberative 
context, unless maybe there is a ratification vote.)

(All the simulations I've seen of two-round runoff have assumed two 
errors: static utilities and a fixed set of voters, thus ignoring 
what are probably the greatest strengths of runoff voting: the effect 
of true preference strength on turnout, and the development of a 
better-informed set of voters in a runoff.) 

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