[EM] Fwd: Two MMV definiions (brief, and ordered-procedure)

[Michael Ossipoff]

Here's my question about MMV:

There are two circumstances in which one would use MMV instead of MAM.
The first is certain, and the 2nd is uncertain:

1. If there were no available and universally-trusted mid-count randomization.

For example, we used to do polling at EM, with ballots actually posted
to EM. In that way, the ballots were completely secure, since each was
an e-mail from its voter.  The signed ballots were visible to all. The
count wasn't automated, but any count result could be checked by
anyone.

But if we'd wanted to use MAM in one of those polls, how could we do
the randomization in a way that all would trust? Mid-count
randomization wouldn't be feasible. We'd just have to use a completely
deterministic count method, and if the voters' ballots result in a
tied-outcome, then so be it.

That situation generally obtains in Internet voting, except at a
really trusted automated-count website like CIVS. I have no doubt
about the security of mid-count randomization in MAM at CIVS.

2. But, even if detrministic counting isn't needed for reason #1, it
could still be desirable. After all, if the ballots and the
count-rule, without any randomization, return a tie, that's what those
voters said. That's the result of their rankings, and of nothing else
(such as randomization). What good would it do to have a unique
winner, and a strict output ranking, if it's a random winner and a
random ranking?

The trouble with #2 is that maybe sometimes the randomization does
more than just make a random winner and a random output-ranking. Maybe
sometimes, a random choice among several defeats, in MAM, can avoid a
result that outright contradicts voter preferences, as interpreted the
RP way. Even if the choice of which of a cycle's defeats to keep or
discard is random, the fact that they're considered, and kept or
discarded, in some order, even if random, might still prevent a worse
contravention of voters' expressed preferences, such as might happen
if they're all kept or discarded together.

If that can sometimes be so, with a particular MMV version, thent hat
could make MAM better than that MMV version, when that's the case.

So, my question is: Do all of the MMV versions discussed so far have
that disadvantage in comparison to MAM? I don't know.

If they do, then doesn't that mean that only circumstance #1, above, is valid?

Michael Ossipoff

On Tue, Dec 10, 2013 at 1:04 PM, Michael Ossipoff
<email9648742 at gmail.com> wrote:
> On Tue, Dec 10, 2013 at 12:23 AM, Anders Kaseorg <andersk at mit.edu> wrote:
>> On 12/09/2013 08:29 PM, Anders Kaseorg wrote:
>>>
>>> On 12/09/2013 08:15 AM, Michael Ossipoff wrote:
>>>>
>>>> Keep every defeat that doesn't contradict a set of kept stronger defeats.
>>>>
>>>> Then, among the kept defeats, un-keep each defeat that contradicts a
>>>> set consisting of defeats equal to it, and of kept defeats stronger
>>>> than it is.
>>
>> Oh, but here’s a new monotonicity failure.
>>
>> Defeats (strong to weak):
>> • A > E, C > D, D > A, E > D
>> • A > B, B > C
>> • C > A
>> The first stage discards C > A; the second stage discards A > E, D > A, E >
>> D, and affirms C > D, A > B, B > C.
>
> That's what stage 3 would do, in the 3-stage version, if cycle AEDA
> still remained in stage 3.
>
> Stage 2 says:
>
> Then, among the kept defeats, un-keep each defeat that contradicts a
> set consisting of defeats equal to it, and of kept defeats stronger
> than it is.
>
> AE and DA, by virtue of cycle jAEDA, contradict only equal defeats, so
> that doesn't qualify them for un-keeping (discard) in step 2l
>
> The only defeats qalified for defeat in step 2 are CD and DA, because
> they contradict eachother (equal defeats) and AB & BC  (stronger
> defeats) in the a cycle ABCDA.
>
> A wins.
>
> After the change in votes, the same things happen, and A still wins.
>
> Even though AB and BC are now unequal, CA is still weaker than both.
>
> MIchael Ossipoff
>
>
>
>
>
>
>> Now suppose support for A > B is increased slightly.
>> • A > E, C > D, D > A, E > D
>> • A > B
>> • B > C
>> • C > A
>> The first stage instead discards B > C; the second stage discards A > E, D >
>> A, E > D, and affirms C > D, A > B, C > A.  This has harmed A.
>>
>> (Empirically, this failure seems much rarer than failures with original MMV.
>> Still, argh.)
>>
>> Anders
>>