[EM] Re: chain climbing methods

[Jobst Heitzig]

Dear Forest!


You defined TACC+ as:
> After finding the (deterministic) TACC winner, create a lottery based
> on random ballot among the set of all candidates that have at least
> as much approval as the TACC winner.

While that is certainly easier than the other randomized version of TACC
which I described (RBACC), I don't think this is the right kind of
randomization. First, it may be far too much randomization since it can
render all candidates possible winners (when the least approved
candidate is the CW!). Second, it may also be too few randomization
(when the TACC winner is the most approved candidate but no CW exists!).

Perhaps I should make clear again why I propose randomization in the
first place: Since it is the only way to avoid that a majority of the
voters has incentive to fuck up the result by producing a fake CW by
voting strategically, when in reality there is no CW! But in order to
make such strategizing a risky thing for at least some members of the
strategizing group, we must make sure that each candidate is beaten by
some of the possible winners. Methods such as Condorcet Lottery, RBCC,
and RBACC accomplish this (at least when enough of the possible rankings
actually ocurr on at least one ballot), but TACC+ does not.


After your proof of monotonicity, you wrote:
> Can you see any holes in that sketch of an argument?

No, I don't think so. I would think that indeed TACC+ is monotonic.


You then proposed another method, VCRB:
> Now here's another lottery method I favor because, although it tends
> to spread the probability around more promiscuously, it has nice
> properties:
> 
> First find the highest approval score alpha such that no candidate
> with approval less than alpha beats (pairwise) any candidate with an
> approval score of alpha or higher.
> 
> Then do random ballot relative to the candidates that have approval
> scores greater than or equal to alpha.
>
> That's it.  Let's call it Viable Candidate Random Ballot (VCRB).

That is perhaps better. By definition, each non-winner is beaten by some
winner. But is also every winner (except a CW) beaten by a winner? And
is it really monotonic?


The new criterion you suggest, Independence from zero probability
candidates, seems to be a natural interpretation of "Independence from
the losers", right? I think it useful. The only other methods I know to
fulfil it are Random Candidate, Random Ballot, and Condorcet Lottery.


On Kevin's example,
  49 C
  24 B (sincere>>A)
  27 A>B>>C
you wrote:
> But I'm afraid that neither TACC nor my modification TACC+ would
> dissuade the B voters from their truncation.

But TACC will elect the fake CW A with sincere votes, but the even less
preferred C with insincere votes: Defeats are then A>B>C>A, approval
scores are A27,C49,B51, hence TACC constructs the chain A<C without
adding B. Hence, the B voters have NO incentive for truncation here!


Yours, Jobst