[EM] Some brief campaign argument

Bart Ingles bartman at netgate.net
Tue Apr 24 00:16:54 PDT 2001

```Martin and Richard both gave excellent replies, so there's probably no
need for me to pile onto poor Craig, but here's my two cents worth
anyway:

Craig Layton wrote:
> (There may be a further reason, that approval is the most mathmatically
> consistent method, but on its own, I don't find this argument persuasive.
> Please let me know if you do, and why.)>

Sure -- how about 'potential for lawsuits' or 'avoiding endless
squabbles over how to interpret the results'?  The fact that approval
avoids inconsistency by collecting minimal information doesn't negate
this.

> 1) Approval is unique in that a sincere vote is always the best strategic
> vote.  However, this is because you are only allowed to express a single
> layer of preferences - if you're preference is A>B>C, you can only express
> the preference A>B or B>C (in addition to A>C).  If you choose to express
> A>B, the system forces you to express B=C, even though this may be far from
> your sincere preference.  It is only a severe restriction on the preferences
> you can express that gives Approval this property, so I don't see it as an

I don't see it as a severe, or even a particularly meaningful
restriction.  The reason is that the ability to express unlimited levels
of preference don't necessarily translate to a result closer to what you
would have wanted.

Suppose a voter starts with his most important cutoff or layer of
preference, corresponding to Approval strategy, and then continues to
make the next most important distinction (dividing either the "approved"
or the "unapproved" sets), continuing until all candidates are ranked.
Each division after the first will have decreasing importance to this
voter.

Now suppose you have several voters doing the same thing.  Assuming all
distinctions are given the same weight, it is likely that one voter's
unimportant distinction will cancel out another voters' top
distinction.  These later, unimportant divisions can be considered
"noise", and the voters' main preferences as "signal".  By encouraging
voters to register too many preferences, you are in effect decreasing
the signal to noise ratio.

Now the question is, "how many preferences are too many" and "at what
point does noise begin to obscure the signal"?  The answer may depend on
the situation, but Approval's generally high SU performance seems to
show that smaller levels of preference tend to be better, or at least
that many levels are unnecessary.

> 2) [...] If everybody uses sophisticated strategy and/or if
> everybody uses an above mean (zero info) strategy then it is true that
> Approval would do slightly better on average in electing the highest SU
> winner.  Arguments that voters will use highly sophisticated strategies are,
> I feel, a little optimistic.  Of course, it is a little irrelevant - zero
> info strategy is the most intuitive, and most likely type of voting, and
> will still result in a higher SU candidate than Condorcet.  Right?
>
> Maybe, but I suspect not.  In a country with plurality voting, approval
> might not change voting habits at all and the vast majority might continue
> to vote for just one candidate.  This is by no means fanciful - I consider
> it likely among voters who don't understand the system very well (and
> perhaps even those who do).
>
> Okay, it's a learning curve and over time, voting habits will change.  When
> the voters finally cotton on to what's happening, will they vote for above
> mean candidates?  There are still many things that might happen.  Approval
> leaves the way open for "vote for everyone except X" type campaigns, where
> the result of the election may bear no resemblance to the highest SU winner
> whatsoever.  In fact, any elections where the voters vote for too many or
> too few will result in a decidedly non-utility maximising outcome.  On the
> whole, I find no evidence to suggest that Approval will, on average, find
> the SU winner more often than a Condorcet system.  The examples that "prove"
> approval will, are based on unreasonable assumptions.

This appears to be a straw-man argument.  I don't know of anyone who
supports Approval on the basis that it finds an SU winner more often
than Condorcet.  It would be enough for me if it was merely in the same
ballpark as Condorcet.

I am interested in the fact that basic "zero info" strategy, or even a
rough approximation thereof, can avoid sincere Condorcet's possible (if
not probable) "zero-SU" outcome.  Such an outcome wouldn't need to
happen very often to cause the method to be repealed (just look at the
controversy surrounding what was essentially a tie-vote in the U.S.
Presidential election).

Of course, my concern with Condorcet's worst-case has softened
considerably over the past several months, with the realization that
simple truncation strategy will probably keep the worst-case from
happening.  But then, if voters need to know about insincere strategy
with pairwise voting, isn't pairwise subject to the same objections as
Cardinal Ratings?  Meaning that these systems are non-minimal, in that
voters are given the opportunity to use strategies which are in some
cases more likely than not to be sub-optimal.

So no, I don't believe voters will have any difficulty with Approval
strategy.  "Above the mean" is the natural tendency, not an obscure
strategy.  vNM utilities are defined by voters' willingness to approve
of candidates, not the other way around.

> I left out number 3) which was approval's simplicity (related to the
> argument that it is a better public proposal).  As I'm pointing it out now,
> I might as well briefly discuss it.  Approval is certainly the easiest of
> the decent voting methods to count and to explain.  There are some economic
> advantages in terms of counting votes and not having to radically change
> voting equipment or proceedures if moving from plurality to approval.  I'm
> willing to conceede that Approval certainly has this going for it.

After talking to several people who have worked or volunteered in
conducting public elections, I don't think this is a minor
consideration.

> However, it isn't necessarily true that Approval is simpler to understand or
> to vote.  Sure, the instructions are simple (vote for as many candidates as
> you like), but it isn't easy for voters to understand how they should vote -
> for how many candidates, what's the best strategy, how should I be using the
> polling information etc.  I would have trouble explaining to someone how
> they should be voting in approval (beyond "just vote for the candidates you
> like").

I don't think it would take much explanation, but try this for a
thumbnail strategy:

(1)  First determine if there are any frontrunners.  If so, vote for
those frontrunners you consider to be "better than average" (among the
field of frontrunners).  Then vote for any minor candidates you like
better than your favorite front-runner.  (Note -- with two frontrunners,
this trivializes to the usual strategy).

(2)  If there are no discernible frontrunners, then vote for the
candidates you consider "better than average".

(3)  Review your completed ballot.  If it seems intuitively wrong, by
all means adjust it until it "feels right."

"As easy as 1-2-3!"

[From a later post:]
> It is worth noting that there is no way of ensuring a consistently high SU
> result.  There are bad SU scenarios in any method - in Approval (with all
> voters using zero info above mean strategy);
>
> Sincere Utilities (out of 100);
> 20% A-60; B-40; C-40; D-0   Approval vote ABC
> 20% A-100; D-40; C-20; B-5  Approval vote A
> 60% D-6; B-3; C-2; A-0      Approval vote DB
>
> B wins in Approval, followed by D then A, then C.  B is the worst SU
> candidate, and D is the second worst.  A (who comes third in Approval) has
> an SU rating which is nearly as high as all of the other candidates
> combined.  Obviously the worst case scenario is pretty much the same for any
> election method.

But why didn't the 60% faction run a candidate it liked better?  This is
a problem with the nominating process, not the election.  By
normalizing, you can at least show the extent to which the large faction
got (or didn't get) what it wanted, given the field of candidates.

> The reason I use absolute SU calculations is because absolute utility is
> what is actually important.

I disagree -- absolute utility is meaningless in the context of
democratic elections.  SU's value was never intended as a surrogate for
AU, at least that I know of.

> It is important to note that absolute can
> diverge significantly from weighted utilities.  I am suspicious of the
> assumption that it will all even out in the end. [...]

Whose assumption?  Certainly not mine.

> As normalised utilities are simply distorted absolute utilities, that are
> increasingly separated from the goal of utility maximisation, it doesn't
> make sense to say that one should pay attention to normalised utilities, but
> not the real utilities they were derived from.  If the goal is utility
> maximisation, you have to accept that the ultimate goal is absolute utility
> maximisation.  If you can't accept this, then you should not support a
> method on the basis of SU maximisation (I note that Richard didn't claim to
> support Approval solely on SU maximisation).

You could just as easily say that absolute utilities are distorted
normalized utilities.  I don't consider myself a utilitarian, but
instead use normalized utilities as a measure of how well voters are
able to make their votes count given a field of candidates (the field
can be an actual one, or an idealized one where every voter has an ideal
"favorite" candidate).  So I'm not really deriving anything from
absolute utilities, and couldn't care less about them.

In the past, and at present for that matter, I asked if anyone had a
better, more descriptive term than "social utility".  So far nobody has
offered any suggestions.  Should we always qualify the term with
"normalized", or even which form of normalization?  I suppose we can
always condense it to a manageable acronym.

Bart

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