[EM] Fwd: Ordering defeats in Minimax

Kristofer Munsterhjelm km_elmet at t-online.de
Thu Apr 27 00:25:25 PDT 2017

```On 04/26/2017 08:09 PM, Juho Laatu wrote:
>> On 25 Apr 2017, at 06:36, Andrew Myers <andru at cs.cornell.edu>
>> wrote:
>
>> 1. WV: (W1, L1) > (W2, L2) if W1 > W2 or (W1=W2 and L2 > L1)
>> [currently implemented] 2. Margins: (W1, L1) > (W2, L2) if W1 - L1
>> > W2 - L2 3. LV: (W1, L1) > (W2, L2) if L1 < L2 or (L1 = L2 and W1
>> > W2)
>
> Those functions make sense to me. I would maybe separate the basic
> WV, margins and LV definitions from the additional tie breaker
> definitions ("W1=W2 and L2 > L1" and "L1 = L2 and W1 > W2").
>
>
>> On 25 Apr 2017, at 11:06, Kristofer Munsterhjelm
>> <km_elmet at t-online.de> wrote:
>
>> I'm usually a wv person, but I think Minmax is more classically
>> associated with margins. Or perhaps I think that because Juho is
>> here and he prefers margins :-)
>
> The strongest argument in favour of margins must be that it is a
> relatively natural preference function. WV and LV are discontinuous
> functions and therefore can not really be called natural. Interest in
> using them comes mainly form strategic defence reasons, not from
> studying what would be a natural way of measuring strengths of
> preference. In addition the results that you get close to those
> discontinuities may appear strange (one additional vote may change

Do you consider Plurality a strategic criterion? It seems to me to be
more of a "natural behavior" criterion: if A gets more first preferences
than B gets any preferences, then B shouldn't win. This seems reasonable
from a natural behavior perspective because A dominates B in some
Approval-ish sense.

If that's a "natural behavior" criterion, then you could say that
margins is more natural from a descriptive point of view (no
discontinuities) while wv is more natural from a criterion point of
view. Though, if we're to go by the apparent popularity of IRV, it seems
that descriptive clarity weighs heavier than criterion clarity.
```