[EM] equal "opportunity" vs "power"

[bql at bolson.org]

On Sun, 6 Jun 2004, [iso-8859-1] Kevin Venzke wrote:

> --- Brian Olson <bql at bolson.org> a écrit :
>> Speaking of "write a new meaning", I challenge that "we all agree"
>> statement. In a recent comment of mine, I claimed that "equal
>> opportunity to vote" is not the same as "equal voting power". You are
>> expressing "equal opportunity to vote" but I think I've seen more usage
>> of 1p1v as "equal voting power".
>
> I read your message but have no idea what you mean by "equal voting power."
> Can you define it?

"Equal Voting Power"
I think it's a stronger statement of what Arrow calls "the condition of 
non-dictatorship". In addition to no one voter being able to decide the 
election, no voter has any more influence in deciding the election than 
any other.

>> Approval may not give exactly equal voting power, some voters will
>> choose more or fewer choices, but it at least gives equal opportunity
>> to vote.
>
> Are you saying that a voter has more power if they vote for more candidates?

On second thought I recall the argument that Approval can be considered 
that a ballot is a YES vote or a NO vote on every choice, and so I guess 
every voter does actually contribute equally to the process, they just 
might not contribute optimally for their utility.

>>> Similarly Borda is definitely NOT "one person, one vote".
>>
>> In the variation where the unranked choices are given the average value
>> of the ranks not used, every voter has equal voting power. ((n(n-1))/2)
>
> If this is true, then equal voting power seems undesirable.  If a person truncates
> then presumably they prefer to give zero points to the truncated candidates.

But then a voter who truncates is given extra power! That power is applied 
negatively against the choices they truncate. The voter may prefer 
whatever they want, but I prefer a fair system.

I suppose 'fair' is up for grabs around here, with the various criterion 
floating around. So, put another way, I want to encourage honest voting. I 
think in the case of a ranked ballot, I want to encourage a total ranking. 
Borda with 0-point assignment for truncated choices encourages truncation. 
Borda with average-unassigned-value assignment encourages a full ranking.

>> Fascinating historical article. So, it seems to me that the primary
>> objection was that in the second (Nth) round of Bucklin _some_ people
>> might be getting additional votes but not necessarily _all_ people.
>> Someone putting down only a first place choice would be given no
>> additional vote in the 2nd round. I would suggest a distribution like
>> for Borda above. This could be countered by saying that a 1st-only
>> ballot then only casts meaningless votes in Bucklin rounds. I say
>> "equal opportunity to vote", and they didn't take it, they effectively
>> stayed at home past the first round. Dunno if that would hold up in
>> court but I'd love to try. :-)
>
> Does it occur to you that a voter might not *want* to give a vote to a second
> candidate?  It's not as though the first choice is eliminated!

Heh, well, I've never been a Bucklin advocate. Again, I don't like 
rewarding truncation, which it seems straight Bucklin does. A similar 
average-unassigned-value variation could fix that. For each round in which 
the ballot does not specify an Nth place, award the 1 additional vote 
fractionally between the choices which were not ranked.

>> Also IRV falls to this logic in the event of an incomplete ballot. If
>> all of an elector's choices that they ranked on their ballot get
>> disqualified, _they get no vote_!
>
> But this would not be fixed by using a "distribution like for Borda above."
> Could IRV be made to have equal voting power, then?

I don't see how IRV could be fixed to meet "equal voting power", but maybe 
I'm just not trying. It does pass what I'd call "equal opportunity to 
vote", where voting with the proper voting strategy (zero info, just how 
you map your preferences onto the ballot, possibly honestly) gives any 
voter the maximum voting power. If everyone votes correctly then there is 
equal voting power. OK, so the fix to IRV is to require total rankings and 
not allow ties. Just hope you don't have to cast a total ranking on the 
California Governor Recall (135 candidates).

>> I claim that a normalized cardinal ratings election satisfies one
>> person equal-power/one-vote.
>
> Why is it important that the method would meet "equal power"?

IMO, "equal power" is fair. With the possible exception that it can wind 
up being sub-optimal for social utility by giving too much vote to people 
who don't really care that much, and it puts an unfair cap on people who 
may be hugely effected by the issue up for vote. But that's really too 
deep a philosophical problem. "One Person One Vote", "Equal Rights", 
"equal protection of the laws" are all established ethical expressions 
that I am comfortable with. So, it seems natural to me that an election 
method should reflect that equality.

>> Really, all of these systems that suffer from incomplete-ballot
>> sub-optimality only provide "equal opportunity to vote" and not
>> necessarily "equal voting power". Normalized CR provides both!
>
> What do you mean by "incomplete-ballot sub-optimality"?

I mean that filing an incomplete ballot, an incomplete ranking, is 
sub-optimal for the expected utility of the voter. A voter is most likely 
to be the happiest with the outcome by casting a fully ranked ballot. (Or 
at least, that's the state of affairs I want, see above anti-truncation 
rants.)

The exception to this could be when there are more choices than a human 
voter has time to find out about and the voting process becomes "I like 
this guy --- 1st. And that one a bit less -- 2nd. Ooo, and that one not at 
all -- Last." and several choices are left unranked. So, how much should 
an election method penalize this voter for not being fully informed? 
Little, I hope.

Brian Olson
http://bolson.org/