[EM] Tideman sort tie-breaker proposal

[Kristofer Munsterhjelm]

On 07/01/2017 11:44 PM, Lucas Dailey wrote:
> I’m working with some talented software developers to build an open
> source, multi-winner  implementation of Ranked Pair/Tideman tailored
> toward budgeting to enable legislators to collectively and fairly rank
> their budget priorities to arrive at a democratic budget. As a former
> municipal legislator (Madison, WI) I discovered first-hand how
> dramatically typical budgeting processes can distort budgets and cause
> worthy initiatives to go unfunded.
>
>
>
> While building our open source software we quickly discovered the sort
> tie problem. I prefer Tideman/RP for public elections because it’s
> relatively conceptually simple compared to its criterion-meeting peers
> (I’m still a fan, Markus Schulze!). I can explain it to voters and
> politicians. However none of the Tideman tie-breaking procedures I’ve
> heard of meet that same criterion of explainability and grounding in
> democracy.
>
>
>
> I have a procedure that I believe meets those criteria, which I
> paraphrase as the “Lost worst: locked-in first” procedure. I like it,
> and I’d love to get feedback on it. I also imagine others have thought
> of it before so any research that’s been done would be helpful. Also the
> procedure wouldn’t work in every scenario so I proposed a secondary
> procedure that is less inspiring but still better than many alternatives
> (and also unlikely to work in every scenario).
>
>
>
> We’re working to have the software ready in the next couple months, so
> any feedback now would be greatly appreciated. And of course if anyone
> wants to contribute to the project we’re happy to work with other
> developers, designers, and mathematicians.
>
>
>
> Here’s a quick deck explaining the procedure:
> https://docs.google.com/presentation/d/1K6VWjMwscspFKRzc2h6YWfWEkqdnQgcLVyVXdTsEbkE/edit#slide=id.p

 From looking at it briefly, I suspect that the secondary tiebreak will 
fail clone independence. Consider a situation where A and B have the 
same average position (I assume by position, you mean rank, i.e. first 
place, second place, etc) so that you choose which is considered better 
by random choice. Suppose that the votes are set up so that the 
candidate you randomly choose will be the winner.

Then suppose A is cloned into A1 and A2 so that everybody ranks A1 above 
A2. That may make A1's average position better than A's, and thus better 
than B's, making A1's win a certainty. Thus cloning A benefitted him.

This is a very sketchy and quick argument; I haven't provided any actual 
scenario that exhibits the proprties I mentioned here. But it seems 
reasonable that cloning could affect the order of average positions for 
the different candidates.