[EM] Truncation-resistant MCA method: MCA-Asset

[Jameson Quinn]

2011/3/1 Andy Jennings <elections at jenningsstory.com>

> Jameson,
>
> I really like these MCA-Asset methods.  If the public thinks asset voting
> is too strange, maybe it is more palatable as a fallback method.  It does
> seem to be a good fit with MCA.
>

Thanks. I've also worked out a version with a guaranteed absolute majority -
which it achieves by adding a "rejected" rating (same as unapproved in
initial count, but do not allow my vote to be given as an asset to this
candidate), and then falling back to a two-candidate runoff round if there
is still no majority after the first round. (A runoff would be rare, because
as long as all candidates care which other candidate wins, at least some set
of candidates must have a rational strategy to avoid a runoff). Also, the
asset sharing is weakened (only preferred candidates can "share" a ballot,
and only by raising "unapproved" to "approved"), so that you can reassure
voters that an unapproved vote will (almost) only ever count against equal-
or lower- voted candidates. (The exception to that, if multiple majorities
are achieved in the asset round, is not strategically favored for the
candidates, so unlikely in real life). Details on this method are below.

>
> Are all candidates eligible to win in the fallback asset election, or only
> the ones who were tied for the highest median grade in the MCA election?
>

For the method below ("Guaranteed MCA"), the latter. For MCA-Asset, I was
tending towards the former, but I would be open to arguments in either
direction. Honestly, I can't make a plausible scenario where this would be
an issue, so I can't get my bearings here.

Here it is:

My favorite systems have few, simply-labeled ratings. For instance, my
current favorite is Guaranteed-MCA, which has the following ratings:

3-*Preferred*. One of my favorite candidates. Either the best possible
result, or one which is better than I hope for from this election.
2-*Approved*. An acceptable candidate. One of the results I can reasonably
hope for from this election.
1-*Unapproved* (default). A result I hope to avoid. However, if a clear
majority winner cannot be found, I would allow my preferred candidate to
decide that my ballot would count against other candidates I'd ranked 1 or
0.
0-*Rejected*. I would never want my ballot to be counted for this candidate
under any circumstances.

Guaranteed-MCA procedure:
Voters rank candidates into the above categories.
If only one candidate has a majority of preferred votes, they win.
If only one candidate has a majority of preferred or approved votes, they
win.
If there is more than one candidate with a majority at a given level, then
the winner is the one of those with the highest range score.
If no candidates have a majority of preferred or approved votes:
    then, a week after the first election, all candidates may "transfer
their votes" to a candidate with more preferred votes than they have. Vote
transfers are transitive.
    Ballots are recounted. If candidate A transferred to B, then all ballots
which rank A 3 and B 1 are counted as B 2 - that is, B gets approval.
    If there are any majority approvals after transfer, the winner is the
one of those with the highest range score on the original ballots.
   If there are still no majority approvals, the two most-approved
candidates in the recount go into a runoff.

This system gives an absolute guarantee that the winner will have at least
the acquiescense of an*absolute majority* of last-round voters - thus the
"Guaranteed MCA" name. It does so as few runoff elections as possible,
because, as long as all voters prefer at least one candidate and all
candidates have some preferences among the other candidates, there is *
always* some rational way the candidates can prevent a second balloting
round. If there is a known pairwise champion (CW) and a known runner-up, the
strong Nash equilibrium is for all voters to vote the ratings as described
(that is, a relatively-expressive ballot), and *the pairwise champion will
win after the first ballot count*. The system has the *minimum number of
rating options necessary to cover the common strategic cases*; this
minimizes the need for triple-thinking which one of two
nearly-practically-equivalent ratings to give a certain candidate. I know of
no other voting system (except for slight variants of this process) which
has these advantages.

Simple voting heuristic for GMCA:
1. Figure out the two frontrunners. (This is NOT a self-fulfilling prophecy
as it would be with Plurality or IRV)
1a. If one frontrunner is part of a group of "near clones" (ie, same party),
consider your favorite member of that group as the frontrunner, and make
sure that the other frontrunner is not in that group.
2. Rank your favorite candidate and all you prefer to both frontrunners as 3
3. Rank your preferred frontrunner as 2 (if they weren't your overall
favorite)
4. Rank anyone you'd prefer to your less-preferred frontrunner as 1.
5. Rank all other candidates as 0.

Note that the above heuristic uses all rating categories. It is a strategic
heuristic, because step 1a effectively pushes clones of your favorite viable
candidate down to rank 1. If there were EITHER more OR fewer ratings
available, the heuristic would require more knowledge of others' voting
intentions than just the two frontrunners in order to come up with a good
strategy which used all rating categories. Thus, 4 ratings is, for this
system, the perfect number.

>
> Andy Jennings
>
>
>  On Sat, Feb 26, 2011 at 2:47 AM, Jameson Quinn <jameson.quinn at gmail.com>wrote:
>
>>  Just a note about non-monotonicity in MCA-Asset: the actual result of the
>> scenario I talked about would be that C voters would defensively approve B,
>> and so B (the PC / CW) would win.
>>
>> 2011/2/26 Jameson Quinn <jameson.quinn at gmail.com>
>>
>> Clearly, "MCA-Asset" as I originally stated it is too complex. So here's a
>>> simpler revision. From here on, "MCA-Asset" will refer to the following
>>> system:
>>>
>>> As before, it's an MCA variant, so the basic MCA rules are the same.
>>> Voters rate candidates into N categories, including the default
>>> bottom-rating category. (I suggest that 3<=N<=5 is plenty for expressing the
>>> basics, without opening up too much room for strategic second-guessing or
>>> pointless hairsplitting.)
>>>
>>> 1. (MCA base) Any candidate who is the only one with a majority at or
>>> above a given rank wins.
>>>
>>> 2. If there are multiple or failed majorities, any candidate may "give
>>> their votes" to any other candidate who has more first-choice votes than
>>> them. If A "gives votes" to B, all ballots are considered to have voted A at
>>> least as high as B. (For example, a B>A>C vote is changed to A=B>...>C, but
>>> an A>B>C vote is unchanged).
>>>
>>> 3. Repeat step 1.
>>>
>>> 4. If there's still multiple or failed majorities, the winner is the one
>>> with the most top-rated votes (original or gifted).
>>>
>>> Here's the advantages. I think this is a great method; along with
>>> Approval and MCA-Range, it is currently one of the 3 favorites I'd advocate
>>> for real world democracies.
>>> A1. Condorcet - If there's a step-1 winner and a pairwise champion (PC /
>>> CW), they will be the same candidate. If there's a majority PC / CW, then
>>> they will win in round 1 in a Nash equilibrium. I think that covers most
>>> real-world cases, and the system seems to give reasonable results even if
>>> these conditions don't hold.
>>>
>>> A2. Semi-honest. Except for the (to me implausible) scenario I discuss
>>> below under "(Non)monotonicity", there is no reason to ever reverse your
>>> honest preferences between two candidates.
>>>
>>> A3. No serious problems with strategies. In particular, this handles
>>> vote-splitting / "intraparty truncation arms race" well. Although there are
>>> many rated systems, including Range and most MCA systems, which share the
>>> other advantages, this is the only such system I know which doesn't tend to
>>> elect C, the condorcet loser, with the following honest preferences:
>>> 30: A>B>C
>>> 25: B>A>C
>>> 45: C>A=B (or C>...)
>>> As in most other rated systems, the A and B voters are tempted to
>>> truncate, bullet-voting to ensure their candidate wins. But in MCA-Asset, B
>>> can then give his votes to A and elect her. Thus, MCA-Asset carries off the
>>> "miracle" of seeing that A is the PC/CW, when only given a pile of bullet
>>> votes, without needing a second balloting round.
>>>
>>> A4. One balloting round, at most two summable counting rounds.
>>>
>>> A5. Good balance of expressivity and balloting simplicity. It's rare that
>>> you're strategically forced to give up expressivity; in most cases, the
>>> "most expressive" ballot is also the "most strategic" one. (In contrast,
>>> Approval is less expressive, ranked methods are cognitively harder to vote,
>>> and Range forces one to choose between expresivity and strategy).
>>>
>>> Here's the disadvantages:
>>> D1: Less simple to describe than Approval.
>>>
>>> D2: The vote-transfer portion could be criticized as undemocratic "back
>>> room deals", although personally I believe it would happen rarely and
>>> even-more-rarely give any result that wasn't obvious from before the
>>> election.
>>>
>>> D3: (Non)Monotonicity
>>> The restriction that a candidate may only give to another who has more
>>> first-choice votes than them is to avoid the "no, YOU give me YOUR votes"
>>> problem. However, like the bottom-up elimination in IRV, it does technically
>>> make the method nonmonotonic. Say there's 1-dimensional ideology, the
>>> candidates are placed
>>> A---B--C--
>>> with each dash or letter representing an equal number of voters at that
>>> ideology. If all voters bullet-vote, then C has the lead, but A transfers
>>> their votes to B and B wins. But C voters, if they're very careful, can give
>>> A enough first-choice votes to prevent A from transferring votes to B. Then,
>>> B is the kingmaker between C and A; but since C is closer to B
>>> ideologically, B may let C win instead of passing votes to A.
>>> I don't think that nonmonotonicity would be a real-world issue, though. I
>>> can't find any cases where it comes up naturally, without strategy. And as a
>>> strategy, it is a very dangerous, and thus unattractive, for three reasons.
>>> First, if enough B voters put A above bottom instead of bullet voting, this
>>> strategy becomes impossible, because it would elect A. Second, even with all
>>> bullet voters, it is easy for C voters to overshoot and elect A by mistake.
>>> And third, this strategy depends on candidate B not passing votes to A,
>>> which B could do either on a whim, or to punish the sneaky C voters.
>>>
>>> Jameson
>>>
>>
>>
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>
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