[EM] Rethinking Burial Detection Runoff

[Kristofer Munsterhjelm]

On 6/15/23 22:17, C.Benham wrote:
> 
> On 15/06/2023 7:17 pm, Kristofer Munsterhjelm wrote:
> 
>> James Green-Armytage has another suggestion for deterring burial: 
>> https://www.jamesgreenarmytage.com/dodgson.pdf
>>
>> I haven't read it in detail, so perhaps the devil's in the details 
>> about "plausible assumptions about how candidate decide". But what do 
>> you think of that method?
> 
> In an earlier article James-Green Armytage discussed different 
> Condorcet-IRV  methods, naming them all after people. I think there was 
> Tideman, Woodall and "Benham".
> 
> Tideman (and "Smith-AV") fails Mono-add-plump and Mono-append. And both 
> Tideman and Woodall are more complicated than Benham.
> 
> https://www.votingmatters.org.uk/ISSUE29/I29P1.pdf
> 
> The "one round version" of what he is now calling "Limited-Round 
> Dodgson-Hare" is the same as Benham except that it specifies a 
> "voluntary candidate withdrawal" option
> and says nothing about whether equal-ranking should be allowed or how it 
> should be handled.
> 
> I don't like candidate withdrawal options because I think the result 
> should be determined as much as possible by voters via their ballots 
> versus the machinations of candidates.

I can see that reasoning; it's similar to why I don't like candidate 
ordering methods (where the published ordering given by the voter's 
favorite completes the ballot).

In a situation where there's an honest CW, it should be fairly well 
known who that CW is... I would imagine. But it's hard to tell how it 
would turn out in practice.

>  From the article you linked you linked to:
> 
>> Further, Green-Armytage et al. (2016) and Durand et al. (2016) both
>> prove that for most single-winner voting rules including Hare, 
>> adding a provision to elect the Condorcet winner when one exists
>> can never make the rule vulnerable to strategy in cases where it
>> was not vulnerable already.
> 
> I'm a bit sceptical about that. I would have thought that it would make 
> Hare (aka the Alternative Vote aka IRV) less vulnerable to Compromise 
> but a bit more vulnerable to Burial.

If I got it right, the claim in Durand's paper is:

Suppose that the winner of an election E according to method M is M(E). 
(An election consists of one or more fully ranked ballots - no 
truncation or equal-rank.)

Suppose that M has the property that a cooperating majority that knows 
how everybody else is going to vote can force any outcome it wants. 
(This is called InfMC and is a weaker majority criterion; Borda passes 
it though it fails ordinary majority.)

Suppose that M* is the method: "Elect the Condorcet winner if one 
exists, otherwise elect the winner of M".

Define that, if, for an election E, it's possible for a group of voters 
who all prefer some candidate A to the winner W elected by M, to make A 
win instead of W by altering their ballots, then E is coalitionally 
manipulable under M.

Then: if M passes InfMC, and if an election E is coalitionally 
manipulable under M*, then it must also be coalitionally manipulable 
under M.

The nature of the manipulation may differ: e.g. it could be burial under 
M* and compromising under M, for instance if strategy is towards the CW 
under M and away from the CW under M*.

(In short, if in a given election, it's possible for a group to modify 
their ballots to change the winner to someone they all prefer to the 
winner, in method Condorcet//M, then it's also possible in method M, if 
M passes InfMC. The strategy, group, and winners may differ.)

If truncation or equal rank is allowed, then the property holds as long 
as "Condorcet winner" is defined in an absolute sense: that for any B 
there exists a group of more than 50% of the voters who prefer A to B; 
but electing "relative" Condorcet winners (ones where more people prefer 
A to B than B to A) can make previously unmanipulable elections manipulable.

(Kevin, Forest: If I got that wrong, feel free to correct it :-)

-km