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

[Chris Benham]

Kristofer,

Thanks for this, but a few things leave me a bit confused and/or disturbed.

> "Mean utility cutoff" is the (relative scale) Approval guideline where 
> the voter approves every candidate above mean utility and disapproves 
> everybody else. Though a relative scale, it's not quite the same thing 
> as "normalized". 

How is it different?   I assume you never have a voter approving all or 
none of the candidates, right?

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?

>
> [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?

> - 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.  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?

What happened to separate entries for BTR,  Woodall and Benham?

Chris B.


On 4/05/2024 5:48 am, Kristofer Munsterhjelm wrote:
> Oops, I numbered my footnotes incorrectly. Let's do that again. 
> (Ignore my last post.)
>
> Here are voter manipulability stats for most of the cardinal and 
> cardinal hybrid methods. The exceptions are:
>     - MJ, because I'm not confident enough about how I implemented it 
> (in particular, what tiebreaker it uses),
>     - Margins-Sorted Approval, because I'm not sure how it works, and
>     - Approval with manual runoff, because it's difficult to model the 
> effects of further discussion between the rounds.
>
> Same testing parameters as the other stats: spatial (Gaussian) model, 
> 4 dimensions, 4 candidates, 99 voters, 500k elections tested, and 32k 
> strategy attempts per election.
>
> As in the last post, I've marked the non-poll methods with an asterisk.
>
> The manipulability values are:
>
> 0.937    *Range(0-5, absolute scale)
> 0.928    Approval (absolute scale)[1]
> 0.710    *Range (0-10, normalized)
> 0.708    *Range(0-5, normalized)
> 0.705    Smith//Range(0-5, absolute scale)
> 0.666    Approval (mean utility cutoff)
> 0.655    Smith//Range(0-10, absolute scale)
> 0.645    STAR
> 0.564    Smith//Range (0-5, normalized)
> 0.557    Smith//Range (0-10, normalized)
> 0.514    Smith//Approval (explicit, mean utility cutoff)
> 0.490    Smith//Approval (implicit, mean utility cutoff)
>
> 0.443    Smith//DAC (mean utility truncation)[2]
>
> Some values from my last post for reference:
>
> 0.480    Copeland//Borda (Ranked Robin)
> 0.417    Plurality
> 0.333    Schulze, minmax
> 0.074    Condorcet-IRV
>
> and for verification, James Green-Armytage's results are:[3]
>
> 0.710    Range (normalized)
> 0.668    Approval (mean utility cutoff)
>
> Range is not part of the poll, but it serves to show the differences 
> between absolute and relative (normalized) scales, and to show that my 
> results are similar to JGA's.
>
> "Absolute scale" gives the voters a common scale to rate on, to model 
> the Range component passing IIA. The voters' utilities in this model 
> are maximum if the candidate is at the same point in opinion space as 
> they are, and minimum at a utility that the spatial model (with random 
> candidates and voters) would exceed 90% of the time. Since this 90% 
> quantile doesn't depend on the candidates who were selected, it's an 
> absolute scale, and 10% of the voter-candidate judgements would be 
> clamped to zero, on average.
>
> On the other hand, "normalized" has the voters rate their least 
> favorite zero and their favorite to maximum.
>
> "Mean utility cutoff" is the (relative scale) Approval guideline where 
> the voter approves every candidate above mean utility and disapproves 
> everybody else. Though a relative scale, it's not quite the same thing 
> as "normalized".
>
> STAR uses a scale of 0-5 inclusive. Since the official STAR ballot 
> text tells the voters to normalize,[4] I've only included the 
> normalized manipulability value.
>
> For most of the other cardinal methods and their hybrids, I've given 
> both 0-5 and 0-10 ballot formats. The 11-slot ballot makes it easier 
> to show a difference of preference, which helps identify the honest 
> Smith set in Smith//Range. However, there's not otherwise much of a 
> difference.
>
> -km
>
> [1] Absolute scale approval has a high tie rate of 5%, so it's 
> possible that it should "really" be worse than Range. My simulator 
> deliberately only checks elections with unique honest winners.
>
> [2] The detailed stats suggest that pushover is a problem with 
> Smith//DAC. However, getting a per-strategy breakdown for cardinal 
> methods is hard due to limitations of my simulator, so it would still 
> have to be verified by other means. The "mean utility truncation" is 
> what makes it cardinal in my simulator's eyes.
>
> [3] Green-Armytage, James (2011). "Four Condorcet-Hare hybrid methods 
> for single-winner elections". Voting matters (29): p. 7; 
> https://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
>
> [4] https://www.starvoting.org/paper_ballots Step 3.
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