Re: Ballot marking rules

From: Steve Chessin <steve_dot_chessin_at_sun_dot_com>
Date: Thu May 13 2004 - 01:16:35 CDT

>Date: Fri, 7 May 2004 23:09:51 -0400
>From: David Mertz <>
>Subject: Re: [voting-project] Re: Ballot marking rules
>On May 7, 2004, at 10:28 PM, Steve Chessin wrote:
>> Based on <>, it seems you use
>> "single" to mean "vote for 1 (only)". The cat catcher election is
>> still one X per candidate, but you call that multi. Political
>> scientists call it block vote.
>Right, I shorten the phrases "single selection" and "multiple
>selection." More or less coming from the way different GUI widgets are
>named (pick lists, drop boxes, etc).
>> <>.
>I don't think so. At least as described on page 5 (actual page 13,
>numbered as 5 after frontmatter) of your reference, it seems to
>indicate "block vote" is a scoring rule, not a marking rule.

It is both. That is, each system is associated with both a marking
rule (how you mark the ballots), and a scoring rule (how you count
the ballots to determine winners). Many systems that have different
scoring rules share the same marking rules. (Party List PR and First
Past The Post, for example.)

>> I think you are confusing /marking/ rules with /scoring/ rules.
>Nah... for this conversation, I have no interest at all in scoring
>rules. They don't make any difference at all for the narrow question
>of how much information is contained in a marked ballot.

Very true. Marking and scoring can be (and should be) separated.

>> Cumulative voting is described at
>> <>. There are N
>> candidates
>> for M seats. You have M votes that can be distributed amongst 1 to M
>> candidates.
>Your reference describes a couple different systems. What is called
>"equal and even cumulative" amounts to the same thing as "multiple
>selection" from a marking perspective. No more than one "X" goes next
>to any one option.


>The "Free cumulative" (which is also more about scoring than marking
>per se) allows multiple votes for the same candidate. The example
>given has five candidates and each voter given five "X"s. Is that a
>uniform equality, or might the quantities be unequal (in both
>(a) Might a voter have 20 votes to distribute among 5 candidates?
>(b) Might a voter have 5 votes to distribute among 20 candidates?
>> You get as many Xs as there are seats to be filled. There is no
>> relation between the number of Xs and the number of candidates.
>Oh, sorry, you answer my above questions. But I'm still not quite sure
>if this is a universal description, or if some jurisdiction might
>decide to have inequalities like those above. If not, why not? More
>votes would seem to let a voter fine-tune preference weights better,
>for example.

Perfect electoral systems are like perpetual motion machines; they
provably don't exist (Arrow's theorem for the one, the laws of
thermodynamics for the other), but that doesn't stop people from trying
to invent them. :-)

While it would be possible to write down the marking and scoring rules
for "20 votes to distribute among 5 candidates" or "5 votes to distribute
among 20 candidates" (the former effectively allowing you to allocate
fractions of your vote, to a granularity of 1/4th as compared to the 5 votes,
5 candidate scheme; the latter an interesting combination of cumulative
and limited voting), I know of no such systems in use in public elections.

One factor to be considered in designing an electoral system is
complexity. (It's not the only factor, of course, but it is an
important one.) The KISS principle applies. You want it to be simple
for the voter. "5 for 5" is simple and easy to understand. If you go
"20 for 5", why not 40 or 100? (Equal and even is even simpler; so
simple, in fact, that many people who voted in Illinois under such a
system didn't even realize that they were using cumulative voting; they
just knew that if they "bullet voted" for one person it helped them.
The same is true in an at-large multi-seat (block vote) race, of
course, but the effect is a lot less, and a lot less predictable as

As for "5 for 20", I'd have to think about what this does to the
threshold of exclusion (the smallest number below which you have no
guarantee of winning a seat). With cumulative voting, the threshold is
1/(S+1), where S is the number of seats. With limited voting, the
threshold is V/(S+V), where S is the number of seats and V is the
number of votes each voter has. I'm not sure what the formula would be
for the limited/cumulative combination you suggest. When I get some
free time....

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Received on Mon May 31 23:17:39 2004

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