[EM] The worst about each system; Approval Preferential Voting (new name for an MCA-like system)

[Abd ul-Rahman Lomax]

At 01:20 PM 5/25/2010, Jameson Quinn wrote:
>What are the worst aspects of each major voting system?
>
>-Bucklin: Bucklin (with equal rankings, of course) doesn't really 
>have a single biggest weakness. It is still technically just as 
>vulnerable to divisiveness as approval; but the trappings tend to 
>hide this fact, and so it shouldn't be as much of a problem in 
>practice. Still, it doesn't have any really strong points either. 
>It's not the best honest system like Range; it doesn't give a 
>Condorcet guarantee; and it's more complex than Approval, without 
>really fixing Approval's greatest flaw.

Bucklin can be tweaked to provide better Condorcet performance. Some 
of the tweaks allow "failure" of the majority criterion and the 
condorcet criterion, when there are multiple majorities in the first 
round. In particular, equal ranking being allowed can be interpreted 
as allowing majority criterion failure, because it is possible that a 
majority prefer a candidate but suppress this preference, even though 
in, say, three-round Bucklin there is very little strategic incentive 
to do so. Bucklin is designed to allow safe expression of first 
preference! Allowing equal ranking without providing high strategic 
incentive for it -- the circumstances where a voter might 
legitimately want to equal rank in first preference when there is 
practically no constraint on simply ranking the favorite top and the 
second favorite (and others, perhaps) in second or lower rank, yet 
the voter has *significant* preference, are rare to impossible.

Which brings up a point. Some technical readings of the majority 
criterion and the condorcet criterion consider that *any* preference 
is sufficient to trigger criterion failure, since the criteria do not 
consider preference strength. Further, generally, criterion failure 
is considered to exist no matter how preposterous or remote is the 
possibility of an actual failure. Absent some objective consideration 
of the significance of criteria failure, the purpose of voting 
systems criteria, to be able to objectively compare voting systems, 
is largely defeated, and the debate becomes which criteria failures 
are more important. It seems odd that, if a preference is not 
*significant*, it nevertheless causes a criterion failure where the 
voter *voluntarily* suppresses the preference. And no voting system 
can divine unexpressed preferences. Taken to its absurd conclusion, 
then, every voting system fails to satisfy the Condorcet criterion, 
for example, since the voters could simply vote for someone else, for 
whatever reason. And no system would satisfy the majority criterion, 
either. The common opinion that plurality satisfies the majority 
criterion assumes that voters vote sincerely for their favorite, but, 
in fact, with plurality, they may *easily* have motives to vote for 
someone else, basically an ignorance, on the part of each voter with 
the necessary preference, that they are, in fact, in the majority and 
that the majority will vote sincerely with them.

The judgment of voting systems is afflicted with this reliance on 
possibly unreliable criteria, in general. Most criteria are generally 
desirable, but even that fails. The condorcet criterion and even the 
majority criterion can be faced with situations where there is a 
better indicated winner, given sufficient information from the voters 
*and the voters will confirm this in a runoff.* This is *especially* 
true with the condorcet criterion, which can indicate a plurality 
winner; implying that the electorate has not settled on a conclusion.


>So, allow me to restate my favored single-winner system, which, I 
>think, avoids all of the major pitfalls above. I call it Approval 
>Preferential Voting (the acronym, APV, is I believe only taken by 
>American Preferential Voting, an old name for Bucklin; and since 
>this system could be considered a Bucklin variant, I think that's just fine.)

It is certainly a Bucklin variant. A less thorough one than what I've 
been proposing, though.

>Voters rank each candidate as preferred, approved, or unapproved. If 
>any candidates have a majority ranking them at-least-approved, then 
>the one of those which is most preferred wins outright. If not, then 
>the two candidates which are most preferred against all others (ie, 
>the two Condorcet winners based on these simple ballots, or the two 
>most-preferred in case of a Condorcet tie) proceed to a runoff.

I see no reason for the reduction of ranks to three from the 
traditional four for Bucklin. For even better performance, I'd 
suggest as many ranks as there are candidates, at least, thus 
allowing full ranking if the voter wishes. In reality, these ranks 
are ratings, if we use Bucklin-ER; that is, they can be voted that 
way, indicating preference strength by the placement of the candidate 
into a rank, relative to the set of rankings. Traditional Bucklin did 
allow this, with the vote of A>.>B being allowed and meaningful. 
(Don't add in the B vote until the third round. That is an indication 
of higher preference strength, and has the appropriate effect.)

>(As a ballot mechanic, parties as well as candidates could be 
>ranked, and any candidate not specifically ranked would default to 
>her party's ranking.)

I'm not going to go there. It's not adequately explained, and would 
be completely inapplicable to nonpartisan elections, which are my 
first priority for reform.


>This method is very simple. I think that the description above, 
>without the parentheses, is simple and intuitive; it uses only 
>concrete terms. It is also very easy for a voter to sort candidates 
>into three rankings; I'd argue that this is the easiest possible 
>ballot task, easier in general than either two or four ranking 
>categories. (Two means too many compromises, and four means too many 
>fine distinctions.)

The voters can easily not use them. Many didn't. This is 
overprotecting voters, taking facility away from them in the name of .... what?

What voters need to know is that, in a Bucklin system, voting for a 
candidate is approving the candidate, providing an action that will, 
under some conditions, elect the candidate with no further ado. Some 
Bucklin instructions may have stated this quite explicitly. In 
Oklahoma, an attempt was made to push for getting a majority by 
requiring voters to add additional preferences, albeit at lower vote 
strength (fractional votes were used for the additional votes). This 
would have been a kind of Range system, but was dumped by the 
Oklahoma Supreme Court based on the mandatory ranking. No voter 
should be coerced into voting for any candidate, by anything other 
than the natural consequence of not participating in pairwise 
elections not involving the more preferred candidate(s).


>It's not quite the same as MCA or any other Bucklin system, since if 
>there are two approval majorities, the preferences, not the 
>approvals, break the tie. This makes APV more lesser-no-harm-like 
>than Bucklin, encouraging voters not to truncate.

Not a tie, Jameson. Multiple majorities, quite a different things. As 
was pointed out, this rule (if multiple majority, the highest 
first-preference vote prevails) leads to proposterous conclusions, 
i.e, to make it completely extreme, one candidate has 51% approval, 
but leads in first preferences (say it's a plurality, and this can be 
quite small, overall), and the other has 100% approval, but the 51% 
candidate wins, through the rule about first preferences. In reality, 
multiple majorities were rare with Bucklin, the problem tends to be 
in the reverse direction, no majority even after all rounds are 
collapsed. My own solution to the multiple majority problem is 
different and more comprehensive, without creating this preposterous 
conclusion of rejecting a candidate clearly approved by all the 
voters, in favor of one who might be quite divisive.

>Note that APV is still not a lesser-no-harm method.

It's called Later-No-Harm. But I guess "lesser" conveys the meaning.

>  But it is in some sense a lesser-minimum-harm method; extra 
> approvals cannot hurt your candidates chances for an outright win 
> OR for a win if there's a runoff, the only way they can hurt is the 
> unlikely situation where they are pivotal in preventing a runoff. I 
> think that this minimizes the divisiveness I discussed with Range 
> above; for instance, in Hawaii, I'm sure the two democratic 
> factions would have had little trouble giving each other sufficient 
> honest approval for the strongest one to win outright.

Later-No-Harm is an offensive criterion. It's really a voting 
strategy, and reasonable *if* the voter has strong preference, and 
not if the voter doesn't.

>Also, if there is no runoff, this method "violates Arrow's theorem". 
>That is, because it does not use a preferential ballot (and thus 
>doesn't have "unlimited domain" by Arrow's terms), it satisfies some 
>Arrow-compatible definitions of the Majority Criterion and 
>Independence of Irrelevant Alternatives Criterion (including 
>clones). (APV as a whole does violates both those criteria, but I'd 
>argue that this would be unlikely in practice.)

When Arrow's theorem is not applicable, it is not violated. (Nor is 
it satisfied.) There is a lot of nonsense out there about Arrow's 
theorem and what it means.

I'm going to lay out a path to reform that starts with simplicity and 
what is known to work, and that does not add cost at first, and that 
may never add cost of any significance.

Environment to be reformed or improved: jurisdiction uses top-two 
runoff, because it is considered important to gain a majority for the winner.

Proposed method: traditional (Duluth) 3-rank Bucklin (4 ranks in 
Jameson's analysis) in the primary. There are various runoff options. 
If there is no majority for the winner, there is a runoff between the top two.

Argument: we know that Bucklin worked and that it was popular. But 
Bucklin does not always find majorities. Bucklin was promoted as a 
way to find majorities without an additional ballot, and under some 
conditions, it failed. This may, then, have provided an excuse to 
dump Bucklin, but, in fact, it would have been more appropriate to 
hold a runoff if needed. Bucklin was replaced with top-two runoff! So 
the method was, at worst, harmless, and it was just that it was being 
used in party primary elections (as the longest-lasting application) 
that made it seem to fail. In fact, as a top two runoff method, it 
probably would have taken a better top two into the runoff, avoiding 
center squeeze or the like. Not that center squeeze is common in 
nonpartisan elections, which party primaries effectively are.)

This reform is Approval with clear majority criterion compliance 
(nobody challenges that). It allows sincere first preference with 
practically no negative consequence. It has not been adequately 
analyzed for Bayesian regret, because some of the implications and 
procedures were not understood, specifically equal ranking in third 
rank was allowed and empty ranks were allowed, and truncation was 
common (but most voters did add additional preferences in major final 
elections that I've seen.) Analysis has often treated Bucklin as a 
pure ranked system, where preference strength did not matter, and 
that is inaccurate.

But this method, of course, fails the Condorcet criterion. Used as a 
primary method, though, that is rather easily fixed, with a possible 
cost, but the situation should actually be rare: Bucklin will usually 
find a Condorcet winner, it appears. Still, until we have a history 
of elections, we won't much know.

Hence, tweaks:

Modify the ballot to add a disapproved (but preferred within the 
disapproved class) rank. Or, ultimately, use a Range ballot. Bucklin 
analysis proceeds down, rating by rating, to the approval cutoff, 
which I suggest be 50% range. Thus Bucklin finds the necessary 
approval level to find a majority, but stops at approval, it will not 
elect by a mere plurality of approvals. Ideally, the ballot has 
sufficient rating resolution to allow complete ranking if that's what 
the voter wants to do. It's simple, and if the voter truncates 
because it gets hard, that's fine. A "hard" preference to find and 
express is weak, and not likely to be important.

Then do additional analysis on the ballot. If a majority is found, 
one is not quite done. The ballots would be re-analyzed to find the 
Range winner and any candidate who beats, pairwise, the majority 
winner, presumably a Condorcet winner (or a member of a Condorcet 
cycle). If a majority winner is beaten by pairwise analysis, both 
would enter a runoff. If the Range winner is different, the Range 
winner would also enter the runoff. Thus it is possible that there 
are three candidates in the runoff, and if write-in votes are allowed 
(it can be a good idea, making the method be, in fact, simple 
repeated ballot, which is fully democratic), the runoff method should 
be able to handle three or four candidates. I'm suggesting using 
quite the same ballot as the primary, just with fewer candidates 
listed (possibly). Initially, because of the political environment, 
I'd suggest that the winner be the Approval winner (even by a 
plurality), so it's Bucklin in that respect, but that *if there is a 
candidate who pairwise beats the Approval winner*, that candidate prevails.

Ultimately, though, runoff rules would be modified as needed based on 
real election experience, hopefully across many elections in many 
jurisdictions.

This method is Condorcet compliant, and the compliance is real, not 
merely a technicality. But for reasons I've explained elsewhere, the 
advantage is actually with the Range winner and one of the others is 
likely to win only if the preference strengths expressed did not 
reveal true voter preference strength, which is possible with range 
because of not only strategic voting but also normalization error.

Yet the method starts out with a very simple ballot, and could 
possibly continue to work with that ballot, and it's a proven one. 
The only real difference here is that it becomes a primary method, 
designed to *reduce* runoffs but not to entirely eliminate them under 
all circumstances.