[EM] Election-Methods Digest, Vol 222, Issue 21

[John Karr]

I looked at something similar when writing Vote::Count 
[https://metacpan.org/pod/Vote::Count]. I couldn't find any literature 
on it and it seemed like a great idea, I called it CondorcetVsIRV or 
Redacting.

When I began to look at how it performed with data from elections where 
Condorcet and IRV do not agree, it almost always chose the IRV winner, 
demonstrating that in most cases where the two don't agree that there is 
usually a later harm effect on the Condorcet side. I think the approach 
could be  valuable as a tool for measuring later harm effects, but not 
worth the complexity for use as a real world method.


> ------------------------------
>
> Message: 3
> Date: Sun, 22 Jan 2023 16:55:15 +0000 (UTC)
> From: Kevin Venzke<stepjak at yahoo.fr>
> To: EM<election-methods at lists.electorama.com>
> Subject: [EM] Adjusted Condorcet Plurality, an interesting new
> 	LNHarm+LNHelp method
> Message-ID:<1920683218.667896.1674406515649 at mail.yahoo.com>
> Content-Type: text/plain; charset=UTF-8
>
> Hello,
>
> Here is the procedure for "Adjusted Condorcet Plurality":
>
> 1. From the submitted rankings, identify the first preference winner (FPW).
> 2. Edit all the ballots so that all preferences below the FPW are removed/truncated.
> 3. On the revised ballot set, check for a Condorcet winner. Elect them if there is one.
> 4. Else elect the FPW.
>
> What's interesting about this is that, like IRV, you can't hurt *or* help a candidate by
> adding additional lower preferences. But this is done without eliminating any candidates.
> The candidate with the fewest first preferences can win!
>
> 26 A
> 25 B>D
> 25 C>D
> 24 D
>
> D wins, no problem. Among other LNHarm methods, MMPO and "LNH Borda" will elect D as well,
> but neither of those satisfies the Plurality criterion. This "ACP" method does.
>
> In other cases IRV does do better:
> 25 A>B>D
> 20 B>C>D
> 20 C>D>A>B>E
> 18 D>C
> 17 E>D
>
> The CW is D, and IRV elects D. But the "adjusted" CW is C, and wins in ACP.
>
> Another:
> 25 A>E>B>C>D
> 21 B>D>C
> 20 C
> 19 D>C>A
> 15 E>C
>
> The CW is C, which IRV elects. But on the adjusted rankings C no longer beats D; there is
> no adjusted CW, and so ACP defaults to electing the FPW, A.
>
> With three candidates, ACP gives the same result as IRV. As the number of candidates
> increases, the Condorcet efficiency and compromise incentive seem to improve over IRV (i.e.
> in simulations), but it's very slight. I guess that if you generate ballots randomly, then
> no matter how many candidates there are, roughly the same percentage of preferences will
> get truncated in the adjustment.
>
> On the downside, ACP loses IRV's satisfaction of Condorcet Loser, mutual majority, and
> Mono-add-top. Mono-raise performance is also worse.
>
> I have added ACP to my LNHarm calculator, so if you like you can experiment and see how
> similar ACP is to IRV. You can click on the "Random scenario" button, so no need to type
> out any ballots:
> https://www.votingmethods.net/lnharm
>
> I found two ways to vary this to create a total of four methods, but I decided the others
> are more complicated while giving less interesting results. One thing you can do is find
> the top two instead of the FPW, runoff between them, and cut all preferences below *either*
> of those two. When there is no "adjusted CW" then elect the runoff winner. This method
> further distorts the "adjusted" form of the ballots since we now truncate under two
> candidates instead of one.
>
> The other thing you can do is produce a LNHarm method without LNHelp, by not simply
> truncating the preferences below the FPW. Instead, for example if your vote is FPW>X>Y,
> then your X>Y preference cannot help X beat Y when considering whether X is the adjusted
> CW, but *does* help X beat Y when considering whether Y is the adjusted CW. While it seems
> like it might (?) be desirable to allow voters to benefit somewhat from these lower
> preferences, all it can do is further help the FPW, which probably makes the method less
> interesting. Example:
>
> 40 A>C
> 35 B>C
> 25 C>B
>
> In the LNHarm-only version, the A>C voters are able to block B from beating C, and C can't
> defeat B, so A wins. Not great: FPP is probably the only other method that picks A here.
> (The normal version of ACP with both LNHs elects B.)
>
> Kevin
> votingmethods.net
>
>
> ------------------------------
>
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> ------------------------------
>
> End of Election-Methods Digest, Vol 222, Issue 21
> *************************************************
-- 

Minds gets scrambled like eggs
Get bruised and erased
When you live in a brainstorm

— Alice Cooper: Hard Hearted Alice
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