[EM] Free riding

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Wed, Sep 3, 2008 at 10:51 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> In general then, any method that acts like Z had never run (when Z is
>> eliminated) would be resistant to Woodall free-riding.
> 
> Right, you can get that benefit from alot of methods.  For example,
> you could do hand counted PR-STV with the following changes
> 
> - restart the count if someone is eliminated (excluding them from consideration)
> - the quota is recalculated at each restart
> 
> This gets almost all the benefit from Meek's method.

At the risk of sounding repetitive, I'll say that this is what the 
multi-round tweak to QPQ does. Whenever someone's eliminated, that 
candidate is permanently excluded, and then the method starts from the 
beginning. Presumably it too would be resistant to Woodall free-riding. 
I don't know if the single-round method is as well.

>> Hmm.. what could be done here? We could try to find out methods that resist
>> Hylland free-riding, or find methods where there are few honest reasons to
>> use the vote management version.
> 
> Ultimately, the problem is that you cannot meet Droop proportionality
> without allowing it to some extent.

The next best thing is what Schulze calls "weak invulnerability to 
Hylland free-riding". A method passes WIHFR if it's vulnerable to 
Hylland free-riding only if to not be so would make it violate Droop 
proportionality.

(He then proves an equivalent condition, but the notation is a bit too 
heavy for me to parse. It seems to be "if voters reorder strong winners, 
then the outcome should not change", where a strong winner is in all 
stable sets, a stable set being a multiwinner generalization of the 
Smith set.)

>> For instance, for a 6 candidate case, there's no way the party
>> could arrange 720 different pseudo-bailiwicks.
> 
> I can't imagine them trying in that case, they likely to just try to
> manage first choice vote management.  Maybe, more seats would protect
> against vote management.

There's one way they could slip this under the radar. The party could 
say that they want all voters to vote A1 > A2 > A3 instead of A1 = A2 = 
A3, ostensibly to perform the same function as list ordering does in 
party list PR. Then, once the people have become used to not using 
equal-ranking, the party can "spice it up" by vote-managing.

>> There's nothing stopping them
>> from doing so, technically, though, and the equal-rank property would make
>> it easier for those who actually want to do vote management to do so, as
>> they can get the majority to equal rank and then just have a small subgroup
>> vote opposite the ordering of the personal voters.
> 
> I think if voters were aware of it, they may react by not giving
> personal votes to that party.

Yes. From one point of view, vote-management based on Hylland 
free-riding uses the strength of personal votes to prop up a collective 
(party) ordering that would otherwise collapse. This can be seen by that 
if there are no personal votes, everybody votes by party, and the party 
is indifferent to which candidates within their party actually gets 
their seats, then equal-ranking would have no disadvantages.

>> For the former, I think that Approval methods would have some inherent
>> safety against this (simply because you can't reorder the candidates).
> 
> You mean proportional approval voting ?
> 
> I think that has strategy issues too.

Not necessarily PAV, but a method that's based on Approval and would 
otherwise be as good as STV, if such a beast exists. What kind of 
strategy can be used in PAV?

>> Schulze's STV is one
>> example of such a method. Perhaps one could make a method based on DSC or
>> DAC in a similar vein (but not PSC-CLE, it scores badly in my simulations),
>> since DAC/DSC works based on sets of candidates.
> 
> I wonder if a range ballot would be useful.  The algorithm then
> optimally converts it into a ranked ballot.
> 
> For example,
> 
> 1) Each voter submits a range ballot
> 2) Each voter's algorithm votes for 1 candidate
> 3) Vote totals are published
> 4) Repeat step 2,3 say 200 times
> 
> Each candidate's score is the sum of votes received in the last 100 rounds.
> 
> This allows voters decide if they want to risk it.  If their favourite
> is ahead, they might decide to stop voting for him.  However, if they
> have rated him much higher than 2nd, they might continue to vote for
> that candidate.
> 
> I am not sure what algorithms to use in 2), one option is to allow
> voters to pick.

Allowing voters to pick the candidate to vote for would be very tedious; 
the algorithm would have to run 200 rounds of voting. If this was a 
single-winner method, you could have used a cardinal ratings (range) 
equivalent of approval strategy A, but I'm not sure how you'd make a 
multiwinner version of that.

More generally, this could be considered DSV. Within the category of 
DSV, one cuold probably make a method that vote-manages on behalf of all 
voters more effectively than any party can. I thought Schulze STV did 
that (because of its mention of "strength of vote managements"), but 
apparently not. A DSV method that does vote management on behalf of all 
voters would either break Droop proportionality or be vulnerable to some 
kind of vote management (although it might be very difficult to do, 
practically).

Another method that would break DP but could work is this: Vote for 
party candidates or independents. After the election, Sainte-Laguë (or 
similar) is used to apportion the seats between parties, with an 
"independent party" for the independents. After that, a party-neutral 
method determines which party candidates get their seats. Parties that 
run vote-management can't gain more seats than they have, 
proportionally, unless they run some candidates as independents. 
However, to do so would look somewhat dirty and the party might lose 
genuine personal votes as a consequence.

To make that method work, you'd have to have a way of counting party 
support, when examining preference orderings, so you know how many seats 
the parties are entitled to. First preference wouldn't work. You could 
have a "you have two votes" ballot, but that could be gamed.