[EM] Notes on a few Later-no-harm methods

[Richard Lung]

Binomial STV is later no harm, unlike Borda count, because uses keep 
values , equivalent to Gregory method, for both election and exclusion 
counts.

Larger elections are more than about just multiplying numbers. Having 
thousands of voters for a few preference perms is not realistic. That 
never happens in real elections.

Likewise, Condorcet cycles (I thought I saw the 3-candidate case in one 
of your examples) are of negligible frequency, especially the more 
candidates and the more voters.

There is no problem with regard to truncations if it involves 
abstentions. All preferences are counted: conservation of information. 
And so have to be given for a binomial stv count. All that happens to 
abstentions including total abstention or NOTA is that they go to a 
vacancy quota for a seat to remain unfilled. I don't think any of my 
examples show this, but the election of "Mr No-one" or Captain Nemo is 
no different in principle from any other election to a seat.

Binomial stv would have the advantage for Australia that last 
preferencs, beyond the number of seats, more or less count against the 
candidate, in an exclusion count, instead of eventually electing some 
unwanted party nominee, on the other side of the political fence.

No equal preferences or "ilections" in elections. I don't know of any 
elections that are ilections (with equal preferences), except from 
theorists.

Regards,

Richard Lung.



On 14/05/2022 10:45, Kristofer Munsterhjelm wrote:
> On 14.05.2022 10:33, Richard Lung wrote:
>> Just a quick reply. I'm not much familiar with notation.
>>
>> Binomial stv is a statistical count that doesn't apply for very small
>> numbers. For that, there is non-parametric statistics. There is no hard
>> and fast rule. I'd say about 32 votes minimum. but that's just a
>> minimum. There is a law of large numbers for better approximations.
> Alright, that's not important to my examples either, so I can easily
> just multiply the numbers.
>
>> I forget the meaning of truncated, kindly explained to me. If you mean
>> what happens with abstentions, they are counted towards the quota for a
>> vacancy.
> Later-no-harm is a criterion that restricts what happens when people who
> leave some candidates unranked, later go on to rank them. For a method
> to pass later-no-harm, it needs to support ballots where not all
> candidates are ranked. Such ballots are usually called "truncated".
>
> A truncated ballot is the kind of ballot that's allowed in optional STV
> such as in New Zealand but disallowed in non-optional STV and AV such as
> the ones used in Australia.
>
> So suppose that we have three candidates running for election: A, B, and
> C. A truncated ballot is one where, for instance, the voter ranks A and
> B and leaves C off the ballot. This is represented in EM notation by
>
> 1: A>B
>
> for a single voter, or
>
> 1000: A>B
>
> if a thousand voters voted that way. Similarly, a voter who votes:
>
> 1: A
>
> is simply expressing a preference for A, being indifferent between B and
> C but considering both to be lower ranked than A. And a voter who votes:
>
> 1: A=B>C
>
> is expressing indifference between A and B, but consider both to be
> better than C.
>
>> With regard to equal preferences, my position is one of both principle
>> and expediency. They are counted by the multinomial theorem. But to me
>> that is an "illection" count, a choosing-in of candidates, not a
>> choosing-out or election.
> Could you give an example? I find concrete examples much easier to work
> with.
>
> In the election:
>
> 3000: A=B>C
> 5000: B=C>A
> 13000: C=A>B
>
> who wins single-winner Binomial STV, and what are the keep and exclude
> values?
>
> Note that the previous election isn't really relevant to my question, so
> if you'd prefer not to answer that one, that's okay. But I would very
> much like to know the keep and exclude values, and winner, for this
> election:
>
> 3000: A>B>C
> 5000: A>C
> 13000: C
>
> That is: 3000 voters rank A first, B below A, and C below B;
> 5000 voters rank A first, C below A, and have not expressed any opinion
> about B except that he's (implicitly) ranked below C;
> and 13000 voters rank C first and have expressed no opinion about
> whether A is better or worse than B, only that both are worse than C.
>
> Now, perhaps your practical implementation of Binomial STV hasn't
> defined what happens in the case of truncation. But then its
> later-no-harm compliance is undefined, not applicable, because
> everything that either fails or passes later-no-harm has to produce
> outcomes when given truncated ballots.
>
> As a final note, if determining the keep and exclude values requires
> some calculation that's very complex in the number of voters, then feel
> free to replace 3000 with 3, 5000 with 5, and 13000 with 13. I'm just
> interested in the outcome of some concrete elections with truncation in
> them, so I can get a handle on Binomial STV's behavior. It doesn't
> *have* to be the ones I listed.
>
> -km