[EM] Manipulability stats for more poll methods (fixed footnotes)

[Michael Ossipoff]

Oh, I see what you meant. You didn’t use the Above-Mean strategy. I just
assumed that that was your intention.

Instead you renormalized the ballots to 0-1, & rounded off a candidate’s
renormalized rating to the nearest integer.

Forgive me for jumping to conclusions. It was just that Above-Mean is the
assumed Approval-strategy that I’ve heard of in simulations. That of course
doesn’t make it better.

I hadn’t heard of it being done as you did it.

Both Above-Mean & Above-Midrange require cardinal estimates. One for the
overall (mean) merit of the candid-lineup; & the other for the halfway
point.

For one thing, Best-Half (Above-Median) is easier, not requiring any
estimate…nothing but your preference-ordering.

Of course the reason why Above-Mean is so much more popular for simulations
is because it’s a better strategy than Above-Midpoint,.

…when you don’t have information for:

Best-Frontrunner

Above-Expectation (based on which candidates you’d rather appoint than hold
the election, or on which candidates’ victories wouldn’t disappoint
you…etc.)

Where the largest merit-gap in the candidate-lineup is (“Largest-Gap”)

Which are acceptable & which are unacceptable

Which you like.

What makes Above-Mean better than Above-Midpoint is that, with no
information about the other voters, our expectation, or significant
differences in acceptability or likability, Above-Mean is what maxiimizes
your expectation.

In addition to Best-Half being the one that doesn’t require anything more
than your preference-ordering, it also has the advantage of maximizing the
number of pairwise-preferences that you vote.

If one doesn’t have the information, feel, or estimates that the other
methods need (including the perception of a particularly big merit-gap),
then Best-Half (Above-Median) would be a good choice.

Speaking for myself, there are unacceptable candidates, & it’s simply a
matter of Approving (only) the Acceptables.







On Sat, May 4, 2024 at 21:14 Michael Ossipoff <email9648742 at gmail.com>
wrote:

> Or approve everyone on the better side of the widest gap among the
> successive candidate-merits.
>
> Even if you don’t have a feel for cardinal-merits, you likely know where
> the biggest gap is.
>
> On Sat, May 4, 2024 at 21:10 Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> Of course, in Approval, if there aren’t other perceived reasons for
>> choosing whom to approve, one could approve above the mean…if you have a
>> feel for what’s average among the candidates. I guess that’s the usual
>> assumption for simulations.
>>
>> If the candidate-lineup is so good that you do above-mean voting, then
>> you’re indeed fortunate.
>>
>> If you’d do that, but you don’t have a feel about the average, & don’t
>> perceive cardinal-merits, then of course you could just approve the best
>> half of the candidates.
>>
>> Maybe that was the assumed Approval strategy to which you were referring.
>>
>> Approval is particularly perfectly matched for an election with
>> unacceptable candidates:
>>
>> Just approve (only) all of the Acceptables.
>>
>> On Sat, May 4, 2024 at 19:27 Michael Ossipoff <email9648742 at gmail.com>
>> wrote:
>>
>>> There’s no reason for the renormalization. Among A, B, C & D (in that
>>> order of magnitude) if B is at the mean, then, with the A=0 & D=1
>>> renormalization, B’s renormalized value is the mean of all of the
>>> renormalized values.
>>>
>>> The position of the mean among the candidates doesn’t change with
>>> renormalization.
>>>
>>>
>>>
>>> On Sat, May 4, 2024 at 15:25 Michael Ossipoff <email9648742 at gmail.com>
>>> wrote:
>>>
>>>>
>>>>
>>>> On Sat, May 4, 2024 at 14:45 Kristofer Munsterhjelm <
>>>> km_elmet at t-online.de> wrote:
>>>>
>>>>>
>>>>> Yes, that's right. But consider a voter with the following utilities:
>>>>>
>>>>> A: 0.57
>>>>> B: 0.32
>>>>> C: 0.23
>>>>> D: 0.08
>>>>>
>>>>> Normalization to two steps fixes the highest value (0.57) to 1 and the
>>>>> lowest value (0.08) to 0 and rounds off the intermediate values after
>>>>> linearly scaling them.
>>>>
>>>>
>>>> Yes. So far, so good. But…
>>>>
>>>> This in essence says that a value is rounded off
>>>>> to 1 if it's greater than or equal to 0.325 (the midpoint between 0.08
>>>>> and 0.57)
>>>>
>>>>
>>>> What? You didn’t average the normalized values. You averaged two of the
>>>> values before normalization. The midrange isn’t usually the same as the
>>>> mean. You used the midrange as the mean.
>>>>
>>>> If you call the top value 1, & the bottom value 0,
>>>> then a rating’s new value is the number that’s the same % of the way
>>>> from 0 to 1 as the old number’s % from.08 to .57
>>>>
>>>> Average of those new values: .4475
>>>>
>>>> You still approve the best two.
>>>>
>>>>
>>>>
>>>> so the 0-1 normalized ballot is
>>>>>
>>>>> A: 1, B: 0, C: 0, D: 0
>>>>>
>>>>> On the other hand, the mean utility is 0.3. So the mean utility
>>>>> approval
>>>>> ballot is
>>>>>
>>>>> A: 1, B: 1, C: 0, D: 0.
>>>>>
>>>>> > 4 "dimensions" sounds like a lot.  What are the "strategy attempts"
>>>>> ?
>>>>> > How much and what information do the strategists have?  Are the
>>>>> > strategists confined to just trying to get their favourites elected,
>>>>> or
>>>>> > any candidate they prefer to the initial winner?
>>>>>
>>>>> The method works pretty much like this, for generating and testing a
>>>>> single election. (I've simplified the exact order that strategies are
>>>>> called upon, but this is in effect what happens.)
>>>>>
>>>>> ==== (Algorithm start) =====
>>>>>
>>>>> Draw candidate positions for each candidate (in this case, each is a
>>>>> point on a 4D normal distribution with mean 0 and variance 1).
>>>>> Draw voter positions for each voter, and create their honest ballots
>>>>> based on the distances between the voter and candidates.
>>>>> Pass the resulting ballots through the method to establish the honest
>>>>> outcome.
>>>>> If there's a tie, skip (because deciding what a strict improvement is
>>>>> when there's a honest tie is ambiguous). Otherwise let the winner be W.
>>>>>
>>>>> For each candidate X who is not the winner W:
>>>>>         For i = 1 to number of strategy attempts / number of candidates
>>>>>                 Set the strategic ballots to the honest ballots.
>>>>>
>>>>>                 For every voter who prefers X to W:
>>>>>                         Replace that voter's strategic ballot with a
>>>>>                         ballot according to a strategy that depends on
>>>>>                         i.
>>>>>
>>>>>                 Pass the modified strategic ballots through the method.
>>>>>                 If X is now a winner, the method is manipulable in
>>>>>                         this election. Return success.
>>>>>
>>>>> If we reach this point without any success, return failure; the method
>>>>> is (probably) not manipulable in this election.
>>>>>
>>>>> ==== (Algorithm end) =====
>>>>>
>>>>> The indexed strategies are
>>>>>         i=0: Compromising (raise X to unique top)
>>>>>         i=1: Burial (lower W to unique bottom)
>>>>>         i=2: Two-sided (do both at once)
>>>>>         i>2: Coalitional strategy
>>>>>
>>>>> The compromising, burial, and two-sided strategies modify the voters'
>>>>> otherwise honest ballots - for instance, compromising changes a
>>>>> strategist's ballot so that X is at unique top and the rest of the
>>>>> ballot is unchanged.
>>>>>
>>>>> The first time the coalitional strategy is called for a particular
>>>>> election, candidate to strategize for, and value of i, it chooses a
>>>>> random number of strategic ballots (between 1 and 3 inclusive). Each
>>>>> strategic voter then picks one of these ballots at random. This
>>>>> simulates strategies where every strategist ballot is equal, as well
>>>>> as
>>>>> ones where there are a few groups each with their own ballot type,
>>>>> thus
>>>>> covering more than JGA's simulations without becoming *too*
>>>>> computationally expensive.
>>>>>
>>>>> So with the setup for the stats that I gave, the full setup for a
>>>>> single
>>>>> method is like this:
>>>>>
>>>>> for j = 1 to 500k
>>>>>         Run the algorithm detailed above.
>>>>>         It returns one of three states: honest tie, success, or
>>>>> failure.
>>>>>         Increment the corresponding counter, call it TIES, SUCCESSES
>>>>> or FAILURES.
>>>>>
>>>>> manipulability = SUCCESSES/(500k - TIES)
>>>>>
>>>>>
>>>>> So to answer your questions:
>>>>>
>>>>> The strategists don't adapt their strategy to the information
>>>>> available
>>>>> to them, even though they strictly speaking have full information.
>>>>> However, they get to try over and over again until they win. If there
>>>>> is
>>>>> a full information strategy with not too many distinct ballots, then
>>>>> this random sampling will eventually find it, given a high enough
>>>>> strategy attempts value.
>>>>>
>>>>> For each non-winner X, everybody who prefers X to the current winner
>>>>> gets to have a go. So not just their favorites: anybody they all
>>>>> prefer
>>>>> to the current winner.
>>>>>
>>>>> >
>>>>> >>
>>>>> >> [2] The detailed stats suggest that pushover is a problem with
>>>>> Smith//DAC
>>>>> >
>>>>> > You don't have enough candidates for a sub-cycle, and so the method
>>>>> > can't fail mono-raise.  How can it have a Pushover problem?
>>>>>
>>>>> I did a bit more checking, and the full preference version doesn't
>>>>> have
>>>>> this high an "other strategy" count. Since I think it's unlikely that
>>>>> the version with truncation would have more pushover than the fully
>>>>> ranked one, I'm going to retract this; most likely it's just an
>>>>> artifact
>>>>> of the simulator's ballot reduction process that falsely attributes
>>>>> the
>>>>> strategy to the "other" category for cardinal methods.
>>>>>
>>>>> >
>>>>> >> - Margins-Sorted Approval, because I'm not sure how it works
>>>>> >
>>>>> > (I struggle to take this at face value.  Probably my promotion of
>>>>> MSA
>>>>> > has convinced you that it is the best method and you were concerned
>>>>> that
>>>>> > your simulation wouldn't do it justice.
>>>>>
>>>>> I'd like to believe both that I have enough scientific integrity not
>>>>> to
>>>>> do that, and that people know I have, too :-)
>>>>>
>>>>> Actually, I was planning on putting MSA at the same level as the other
>>>>> "I don't know enough about these or their dynamics" methods (double
>>>>> defeat Hare, MSMLV, and Max Strength Transitive Beatpath).
>>>>>
>>>>> > But our expert doing the
>>>>> > simulation claiming he can't understand the method isn't a good look
>>>>> for
>>>>> > its proposability.)
>>>>> >
>>>>> > Why didn't you simply ask me to explain it to you?
>>>>>
>>>>> I think it's the sorting phase that does it. My vague idea of how it
>>>>> works is that you essentially run a sorting algorithm on intermediate
>>>>> values, and that seems a little too complex to me. But I might just
>>>>> have
>>>>> got it wrong and then the initial impression of it as an intimidating
>>>>> method stuck.
>>>>>
>>>>> Ted Stern pointed me at the Electowiki article for MSA, which in turn
>>>>> led me to his Python implementation. I might port it if I have time,
>>>>> but
>>>>> I feel a bit exhausted after gathering all these stats. We'll see :-)
>>>>>
>>>>> > What happened to separate entries for BTR,  Woodall and Benham?
>>>>>
>>>>> They're in the other post. I didn't want to add them all to the post
>>>>> that was intended to focus on the new results. That's why I said "some
>>>>> for comparison" - the others are here:
>>>>>
>>>>>
>>>>> http://lists.electorama.com/pipermail/election-methods-electorama.com/2024-April/006029.html
>>>>>
>>>>> I could post all the stats - ordinal and cardinal methods' - in a
>>>>> summary post if you or other EM members would like.
>>>>>
>>>>> -km
>>>>> ----
>>>>> Election-Methods mailing list - see https://electorama.com/em for
>>>>> list info
>>>>>
>>>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240505/1b9e9751/attachment-0001.htm>