[maemo-community] Score voting (aka range voting) vs STV

From: CLAY SHENTRUP clay at electopia.org
Date: Tue Jan 27 06:06:17 EET 2009
Dear Maemo Community,

My name is Clay Shentrup, and I am an election methods activist affiliated
with ScoreVoting.net, and briefly mentioned in the William Poundstone
Book *Gaming
the Vote*.

I understand that you are considering which voting method to use for your
internal elections, and the following forwarded message is my attempt to
counter some of Dave Neary's initial criticisms/concerns about score voting.

The terminology can be a bit complex, so to be clear:
*Score voting* (abbreviated "SV", aka "range voting"/"RV") is a
single-winner voting method in which the candidates are rated on a scale,
and the one with the most points or "best average" is the winner.
Reweighted score voting* (abbreviated "RSV", aka "reweighted range
voting"/"RRV") is a multi-winner version of score voting (SV is identical to
the single-winner case of RSV) in which SV ballots are reweighted after each
round, to achieve proportional representation. It is explained in detail by
the Princeton math Ph.D. who invented it, here:
Single Transferable Vote* (abbr. STV) is a proportional representation
election method that can be used to elect one *or more* candidates, and is
explained mathematically here:

*Instant Runoff Voting* (abbr. IRV) is the single-winner case of STV,
compared to score voting here: http://scorevoting.net/CFERlet.html

In comparing SV to IRV, the simplicity and superior performance of SV is
easy to demonstrate via Kolmogorov complexity (to assess simplicity) and
Bayesian regret (to assess average voter satisfaction - "performance"). This
gets more complex when we use the multi-winner proportional forms of these
two methods, but as the *RRVj.html* link above explains, multi-winner score
voting is simpler than multi-winner STV, and satisfies a specific
proportionality theorem, which STV does not. I go into considerably more
depth with Dave in the following forwarded message.

Clay Shentrup
San Francisco, CA

---------- Forwarded message ----------
From: CLAY SHENTRUP <clay at electopia.org>
Date: Sat, Jan 24, 2009 at 23:32
Subject: Re: election method
To: Dave Neary <dneary at maemo.org>
Cc: rabelg5 at gmail.com, vdv100 at gmail.com, timeless at gmail.com, andrew at bleb.org,
benson.mitchell at gmail.com


Thanks for taking the time to express your concerns and reservations about
score voting. I agree with you that ease of voting and verifiability are
important considerations. You also note the importance of voter satisfaction
regarding the actual elections results. When considering a choice among
several alternative voting methods, one might ponder how much extra work the
average voter is willing to put up with for a given amount of increased
happiness with the average election result. But the nice thing about score
voting is that it doesn't force such a dilemma, as it gives increased
happiness *and* simplicity. From http://scorevoting.net/Lorenzo.html

Range voting is *simpler* in these objective senses:
A. Write a range voting computer program and an IRV computer program
(preferably with error-checking of the inputted votes). The range voting
program will be shorter and will run faster, assuming essentially any
reasonable programmer does it. (This, called "Kolmogorov Complexity" is the
standard objective metric used by scientists to assess "simplicity.")
B. Range voting runs on *all* today's voting
machines<http://rangevoting.org/VotMach.html>without any modification
(including non-computerized machines). IRV does
C. Voters experimentally make fewer ballot-invalidating errors when using
range than when using IRV.
D. Not simple enough for you? Okay, range is a parameterized class of
methods, with the parameter being the number of ratings. The simplest kind
of range voting is called "approval voting." It has only two ratings, Yes
and No. Approval Voting is absolutely the simplest major voting system
reform possible. It requires no changes to ballot forms; all it requires is
eliminating the "no-overvote" rule, thus actually *simpifying* the rules
versus now.

I repeat, STV/IRV (and presumably *all* ranked voting methods)
*increase*the rate of spoiled ballots compared to plurality voting, by
a factor of
around *seven*. (http://scorevoting.net/SPRates.html) - whereas score voting
*decreases* them. Also score voting is mathematically simpler, and easier to
tabulate than IRV - and the same analogous claim is true of reweighted score
voting (the proportional variety, henceforth referred to as "RSV") as
compared to STV. So SV/RSV also is more "transparent" and "verifiable" than
STV/IRV, to the extent that those terms can have any objective meaning. This
is why I find it particularly ironic that you cite simplicity and
verifiability as reasons for supporting STV/IRV over RSV/SV.  (I should also
note that RSV (aka RRV) satisfies a proportionality theorem, whereas STV
does not. This is explained at http://scorevoting.net/RRVj.html .)

Now you eventually get into the more complex, and notoriously misleading
issue of *strategic voting*. I'll just quote your words for reference:

It is confusing for the electorate, who have to start thinking like game
> theorists to ensure that their actual will is reflected in their vote.

This is a typical criticism of score voting that I consider to be highly
(unintentionally) misleading. The most notable thing you're ignoring is that
strategic voting is *also an issue with STV/IRV*, as is explained here:

But let's ignore all that excessively mathematical banter for the sake of
argument, and brevity. There's a much simpler problem here, the gist of
which I will convey via another simple analogy:

Imagine that in universe-X, each human receives 1 hour to spend in a
euphoric state of happiness. Now imagine that in universe-Y, each human
either receives 2 hours to spend in a euphoric state of happiness, or if he
spends some time doing a really hard math problem, he gets 3 hours. Now *you
* complain that universe-Y is bad, because it "confuses" all those people
who work to get the full 3 hours. Well, I point out the obvious. If those
people don't like doing that hard math problem *then they don't have
to!*They can simply do
*nothing* and still be happier in universe-Y than in universe-X. So taking
the analogy back to voting, you are basically complaining that score voting
is "bad" because a voter has to spend time devising a good strategy in order
to increase his happiness from what it would be with an "honest" vote. But
you're ignoring that he was *already better off* with an honest score voting
ballot than with an STV/IRV ballot.

To put it as bluntly as possible, let's say you ask the voters to choose
from the following, placed in order of how statistically well off they would

1) Vote honestly using STV/IRV
2) Vote strategically using STV/IRV
3) Vote honestly using RSV/SV
4) Vote strategically using RSV/SV

Any rational ("sane") voter would want to use option 3 or 4. Even if you
believe that 1 and 2 have equivalent complexity (because you cannot
accept/fathom that STV/IRV is susceptible to strategic voting), there is
still no reason for a voter to prefer *either* of the first two options to
his favorite of the latter two.

Again, your argument is that voters should prefer options 1 and 2 over
options 3 and 4 *if* they prefer option 3 to option 4. Well, that doesn't
make sense. If you think I'm mis-stating your argument, please correct me.

It is confusing when the results are published, and can result in
> counter-intuitive results where someone who is no-one's favourite
> candidate ends up topping the poll.

Again, a very misled line of reasoning, because:

1) STV/IRV can elect a candidate who was the favorite of *only 2 voters*, *no
matter how many voters there were*. I do not see any particular reason to be
appalled that Smith won the election being favored by *0* out of 1,000,000
voters (in score voting), but to *not* be appalled that Smith won the
election being favored by *2* out of 1,000,000 voters with IRV. (See
http://scorevoting.net/IRVamp.html#bad for proof of this.) And since *either
* scenario is incredibly unlikely in practice, I do not see how this
consideration can be a high priority.

2) There is no *rational* reason for it to be "confusing" or
"counter-intuitive" for the winner not to have been any voter's favorite. It
is mathematically *proven* that the "best" candidate may not necessarily be
anyone's favorite - *no matter how you define "best"*.

3) IRV can have *vastly* more "counter-intuitive" results, such as where a
candidate lost because too many of his supporters showed up to vote for him.
(I.e. more of them could have stayed at home, and not voted, and then he
would have won -- http://scorevoting.net/IRVpartic.html )

If you want to really talk about counter-intuitive results, STV/IRV takes
the cake. Here's more (math heavy):

> Preferential voting, where you rank candidates up to the point where you
> don't want to vote for any more candidates, is an easy system for the voter,
> and reflects the will of the electorate pretty well.

I already demonstrated that it is actually more complex in essentially every
way, in objective terms. Also the "abstention" concept in score voting is a
simplification that is unrivaled by anything in STV - because if you
"abstain" it's identicaly to rating a candidate tied-for-last.

Furthermore, I would not say that STV reflects the will of the electorate
"pretty well". If you look at these Bayesian regret figures (which are
typical, and not artificially selected to make SV look good), IRV is
substantially worse than score voting and other methods -

This is a *huge* difference in the voters' expected satisfaction. It is more
difficult to perform Bayesian regret calculations on multi-winner voting
methods, but the performance of a multi-winner voting method in the
single-winner case is perhaps the best relative comparative criterion. At
the very least, the proven proportionality and simplicity of RSV make it a
superior option to STV in every quantifiable way.

The counting system used when running a preferential election balances
> practicality, simplicity and mathematical efficiency.

Score voting is superior in all those respects, in an objective,
mathematically quantifiable way.

Condorcet or some other run-off counting system might generate correct
> results, but I have
> never been able to understand the published results of the DPL elections,
> and I have a maths degree.

Kind of a red herring in this discussion, not that I mind.

And so, my preference for a voting system balances these three things which
> I think are important, in order of their importance: STV is easy for the
> voter, easy to follow during the count, and produces results which reflect
> well the will of the electorate.

Score voting is better in all three ways. I can pretty much say that is just
a plain point of fact, although I'm happy to hear your arguments to the


clay shentrup
phone: 206.801.0484
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