majority? (Was Re: [ER] A Summary of the Problems with the

Steve Eppley seppley at
Thu Feb 20 19:07:41 PST 1997

Mike Saari asked:
> Is there a voting system which allows/encourages honest voting yet
> has any possibility of producing a Chocolate winner? 

There's no way to tell that the 40% who voted "apple=awful" were
honest about it.  They have a clear incentive to exaggerate, if the
voting method will tally the dishonestly exaggerated "apple=awful"
and thereby elect their favorite chocolate instead of the group's
best choice.  So, sadly, the two criteria in the question appear to

The context of Mike's question has some misleading elements, but
there's a valid question underlying it.  His context makes it appear
that the status quo choice of "eat no pie" is a punishment for the
group, but in actuality it would mean saving the cost of the pie and
maybe spending it on a better investment than a self-gratifying
dessert.  So the fact that 40% of the voters consider apple to be
far worse than the "no pie" status quo is beside the point; what 
is at issue is really that the 40% consider apple to be far worse 
than *chocolate*:

   60:   apple > chocolate
   40:   chocolate >> apple
(The symbol '>>' means "is preferred MUCH more than".)

(I think Mike understands that likes and dislikes are really
relative preferences, not absolutes--he acknowledged it in a 
message in priorities at he still frequently 
uses misleading language.)

I think Mike should be asking this question:  is there some voting 
method which will elect B with the preferences
   51:  A > B
   49:  B >> A
yet won't encourage voters to exaggerate preference intensities?

As I said at the top, to my knowledge the answer is No.  And in a 
conversation I had with Prof. Ordeshook at Caltech some weeks ago, he 
briefly raised the possibility of voting preference intensities and 
quickly dismissed it as meaningless and unworkable.  (If Mike wants 
Ordeshook's email address, I'll give it to him.)

* *

There's no reason to believe that one person's feeling that
"it's far better to spend $5 on a chocolate pie than save the
$5" corresponds identically to another person's feeling that "it's
far better..."  What's really being compared if one voter says "I
somewhat approve of buying the pie" and another says "I somewhat
oppose buying the pie"?  If one of them has been taking tranquilizers
and so has deadened feelings, or another has dropped acid so all pies
would seem to be most excellent, their votes may be more or less
"intense" than others'.  If someone is opinionated and strong-willed,
or tends to see things in black and white, expect very intense votes
which will work in his/her favor, to the detriment of voters who are
more moderate in reporting their opinions.

* *

Another point:
Suppose voters V1 and V2 have *identical* evaluations of two
Presidential candidates X and Y: they both agree that X would
increase the country's wealth by $1 trillion and that Y would cost
the country $2 trillion.  But there's a third candidate Z they
disagree on: voter V1 thinks Z will increase the country's wealth
by $10 trillion, but voter V2 thinks Z will decrease the country's
wealth by $5 trillion.  

Mike didn't stipulate that every voter must use an identical scale. 
Perhaps we could use an open-ended ballot where every voter is asked
to report their $ estimates, and we can average the utility

    V1:  X=  $1T            V2:  X=  $1T
         Y= -$2T                 Y= -$2T
         Z= $10T                 Z= -$5T

Z wins?  Looks reasonable, but there's a strong incentive for voters 
to misrepresent their evaluations.

If all the voters are asked to report a number from -10 to +10 for 
each candidate, their "natural" votes would be something like:
    V1:  X=  -5            V2:  X= +10
         Y= -10                 Y=   0
         Z= +10                 Z= -10

X wins?

What can society learn about how the voters feel about X and Y if
voters will give X and Y different scores even when their
evaluations of X and Y are identical?

* *

One more point: the lesser evil voting dilemma.  The
"apple=excellent+, chocolate=excellent" voters don't feel much of 
a dilemma, since this is a low stakes vote and the "lesser evil"
chocolate is about as good as the favorite apple.  This scenario may
be the norm in a Baskin-Robbins, where I'd enjoy even my least-liked 
ice cream flavor, but it's not going to be like this when voting on
high stakes issues.  When pre-election opinion polls indicate that
one of two choices are likely to win, and that other choices are
unlikely to win, then the voters will have a strong incentive to
misrepresent: they'd likely vote +MAX on one and -MAX on the other,
ruining the important mandate information.

And a mathematical analysis shows that even with no pre-election
opinion poll data--no knowledge of how others will vote--it makes
sense to vote +MAX or -MAX on every choice (just as one does with
the Yes/No approval method), no matter what the actual preference 
intensities, as this optimizes the voter's expectation.  (I posted 
this analysis in development at last summer, and will 
forward it to the EM list if requested.)

* *

Maybe there's some other method with satisfying properties.  How
about having the voters report intensity numbers, and tallying the
numbers two ways:

  Tally 1. Ignore the numerical distance between the choices: 
           just tally the preference order info using Condorcet.

  Tally 2: Don't ignore the numerical distance between the choices:
           maybe sum each choice's ratings and select the one with
           the highest sum.

  If both tallies select the same choice, it wins.
  Else vote again (maybe with a simple Approval ballot), on 
  just the two selected choices.  

The first ballot info may help convince the apple voters to re-vote
apple=chocolate (or abstain, which takes less labor), if they believe
the "chocolate >> apple" intensities were sincere.  This would allow
chocolate to win.  But if they don't believe those votes were
sincere, and still want apple, is there a good reason to deny them
apple?  Should a persistent majority be stoppable by a dishonestly
exaggerating minority? 

* *

Another possibility is to impose a supermajority requirement on
certain decisions where the group believes majority is insufficient, 
but without asking voters for preference intensities.  

This, of course, would privilege the status quo.  In politics, this
could mean privileging the haves over the have-nots.  It's fine for 
conservatives and those who have been thriving, but there are a lot 
of people--maybe a majority?--who may have needs or reasonable 
expectations which aren't being met.

I don't think supermajority is relevant to electing representatives,
and it's probably a bad idea to use it to elect important executive
offices which mustn't remain empty.  It's a terrific idea for
confirmation of judges and other appointees, though.

Supermajority doesn't entirely satisfy the question, though:

   99:   apple=     excellent+
         chocolate= excellent

    1:   apple=     awful
         chocolate= excellent

   Elect chocolate?

There are enough discussions of majority vs. supermajority going on
in other maillists that a parallel discussion in EM probably isn't

* *

Another possibility is for the 40% to threaten to leave the group, or
take some other action that demonstrates their sincere intensity, as
historically has been done.  Constructing placards reading "Apple pie
is awful!" and "This group is unfair to apple-haters!" and picketing
the picnic comes to mind...  Next picnic the choice will be better.

---Steve     (Steve Eppley    seppley at

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