[EM] MAV on electowiki

[Abd ul-Rahman Lomax]

At 11:31 AM 6/26/2013, Chris Benham wrote:
>Jameson,
>
>I don't like this version at all. These methods all have the problem 
>that the voters have a strong incentive to just submit approval 
>ballots, i.e. only use the top and bottom grades.

"Strong incentive" requires "strong preference."

The method provides limited later-no-harm protection. That protection 
is not -- and should not be -- absolute.

We know from real Bucklin elections that many voters will add lower 
preferences. No voting system is going to overcome the tendency of 
voters to bullet vote.

>Your suggested way of determining a winner among candidates who 
>first get a majority in the same round only makes that incentive a 
>bit stronger still.

No, it reduces the incentive to bullet vote. That is, it make a 
decision to add a vote at a lower rank easier. Under the condition 
that the "tiebreaker" is active, the lower vote cannot cause the 
favorite to lose, because it is removed from consideration. (I have a 
sense that there is a rare condition where this may not be so, but it 
would not be something that voters would rationally worry about.)

There is a problem, though. Multiple majorities are likely to occur 
with frontrunners. Most additional votes for the frontrunners are not 
so likely  to come from the supporters of the other frontrunner. They 
will come from supporters of minor candidates. MAV, then, may 
disregard these additional votes by backing up. Not good.


>I agree with a Mike Ossipoff suggestion, that we elect the member of 
>that set of candidates with the most above-bottom votes.

There are four basic possibilities, outside of runoffs, given the 
appearance of a multiple majority at a canvassing level.

1. Elect the most-approved candidate, considering all votes 
above-bottom as approvals. Or considering all approved categories as 
approvals, if it is possible to vote an unapproved category 
above-bottom. Ossipoff's idea.

2. Elect the candidate with the most votes at or above the canvassed 
rating level. Basic Bucklin.

3. Elect the candidate with the most votes above the canvassed level. MAV.

4. Use a graduated median, which is a compromise between 2 and 3.

5. Elect the majority-approved candidate with the highest score, 
considering all the votes as scores (probably Range 4.)

If the election fails to find a majority, going through the approved 
categories, the election may then, I'd suggest, flip to pure Range 
evaluation. Candidate with the most votes, considering the ranked 
votes as Range ratings, wins. This is a plurality result, there is no 
majority approval.

This, the last option, is really similar to Mike's suggestion, except 
that the canvassing uses the preference strength data that is 
intrinsic to a sanely-voted Bucklin ballot. It does provide limited 
later-no harm protection, because the later votes are at lower 
strength. The problem with the Ossipoff suggestion is that all later 
votes, if used, are taken at full strength. His is an Approval 
option, I've just suggested Range.

So the method does two things. It lowers the approval cutoff until a 
majority is found, if one is going to be found. It then uses Range 
amalgamation to deal with the possibility of multiple majorities. It 
avoids considering a "better evil" category as an approval, it only 
uses the preference data from such a vote as a small contribution to 
a social utility sum.

>Also, given the strong truncation incentive, I think 5 grades is one 
>too many. In my opinion 4 grades would be adequately expressive.

Range 3, but with the preference strength between a disapproved 
candidate and a minimally approved candidate being equated to the 
minimally weak preference strength between a Favorite and a second 
preference. (i.e., second preference is voted 2nd rank, instead of third rank.)

That's highly unrealistic. I've suggested that a Bucklin ballot is a 
Range 4 ballot, realistically, with the next-to-nadir ranking being 
unexpressed. So the rating values are 1.00, 0.75, and 0.50 for all 
standard Bucklin votes. 0.50 is the minimal approval cutoff, 
suggestive of "election expected utility." No gain, no loss. And then 
we can add that rating in, but *not as an approved rating*. It is not 
used for the ordinary Bucklin evaluation, seeking a majority. But 
with methods 1 and 5, that rating would be used. Method 1 does a bit 
of violence to the preference expression, pulling up what is sanely 
half of the expected election utility to full approval.

>My favourite Bucklin-like method is "Irrelevant-Ballot Independent 
>Fallback-Approval" (aka IBFA) that I introduced in May 2010.
>
><http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html>http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html
>
>"A, B, C, D" are probably better names for the ratings slots than 
>the "Top, Middle1, Middle2, Bottom" in that post.
>Comparing it to Bucklin, it meets Independence from Irrelevant 
>Ballots which means that adding or removing a few ballots that 
>bullet-vote for nobody (ignored on all the other ballots) can't 
>change the winner.
>
>The small "price" paid for this (apart from greater complexity) is 
>that it fails Later-no-Help. That is mostly a benefit because it 
>weakens the truncation incentive.
>
>The other advantage of IBIFA over Bucklin is that it is far more 
>likely to elect the Condorcet winner. If the winners are different 
>then the IBIFA winner will always pairwise beat the Bucklin (or 
>Majority Judgement) winner.

Thanks for the discussion, Chris. Now, we need a name for 
Range-evaluation Bucklin.

Notice: this is pure Bucklin *unless* there are multiple majorities 
or majority failure. It is similar to Oklahoma Bucklin, which did 
assign fractional vote values to the lower preference votes. (The 
ranks were 1, 1/2, 1/3).

I'm now seeing this as ideal from a democratic process perspective.

1. A majority is sought. "Majority" is a Yes/No decision, it is not 
evaluative. The basic democratic princile is that of majority 
*consent.* By voting to approve a candidate, singly or with others, 
the majority is explicitly consenting to the election of that 
candidate. Bucklin amalgamation allows voters to determine where in 
the process to introduce additional approvals. Thus it improves their 
ability to express preferences.

2. If majority choice is not clear, then Range amalgamation is used. 
The Bucklin amalgamation process should encourage sincere rating with 
reference to the voter's election expectation. The additional 
unapproved rating above bottom allows participation in election 
choice below election expectation. Range results, in theory, will 
usually predict the results of a runoff. So if a plurality result is 
to be accepted, a result that would be predicted from a runoff is 
superior to some other result.

This method, then, could be used, the same, in a runoff system, with 
top-two range selecting the nominated candidates for the runoff, and 
with a pairwise test to see if any other candidate can beat the top 
two. If so, that candidate would also be nominated. If there is a 
Condorcet cycle, the top two members of the cycle, per range 
amalgamation would be nominated, plus the Range winner, if not 
already included.

As a runoff method, with write-ins allowed, sincere voting remains 
fully possible and safe. A sincere categorization into the five 
categories, then, becomes important for voters.

The "meaning" of the vote is an assignment of utility value to the 
election of that candidate, at closest value to the fractions 
expressed. Voters *may* bullet vote, but are then risking lack of 
participation in the final decision. You pay your vote and you take 
your choice. And this is *approval voting*, unless it defaults to 
range because of no majority -- or multiple majority.

In a runoff, I'd expect a majority to be routine, multiple majorities 
not uncommon, and majority failure rare.

No more original content below.

>Jameson Quinn wrote (19 June 2013):
>
>Here's the current version of the article. Note the new paragraph on 
>strategy at the bottom.
>---------
>
>Majority Approval Voting (MAV) is a modern,
>evaluative<<http://wiki.electorama.com/wiki/Evaluative>http://wiki.electorama.com/wiki/Evaluative> 
>version of Bucklin voting 
><<http://wiki.electorama.com/wiki/Bucklin_voting>http://wiki.electorama.com/wiki/Bucklin_voting>. 
>Voters rate each candidate into one of a predefined set of ratings 
>or grades, such as the letter grades "A", "B", "C", "D", and "F". As 
>with any Bucklin system, first the top-grade ("A") votes for each 
>candidate are counted as
>approvals. If one or more candidate has a majority, then the highest 
>majority wins. If not, votes at next grade down ("B") are added to 
>each candidate's approval scores. If there are one or more candidates with a
>majority, the winner is whichever of those had more votes at higher 
>grades (the previous stage). If there were no majorities, then the 
>next grade down("C") is added and the process repeats; and so on.
>----