[EM] Arrow's theorem and cardinal voting systems

fdpk69p6uq at snkmail.com fdpk69p6uq at snkmail.com
Fri Jan 10 21:24:58 PST 2020

On Thu, Jan 9, 2020 at 11:46 PM robert bristow-johnson wrote:

> "strong preference" vs. "weak preference" implies a Score ballot.

Usually, but not necessarily:

my question that i have asked the Score Voting or Approval Voting advocates
> years ago remains: "How much should I score my second choice?"

If asked to rank three ice cream flavors, my preference would be Strawberry
> Chocolate > Garlic.

If then asked to choose between:

1. Chocolate
2. A mystery box with a 75% chance of containing Strawberry and a 25%
chance of containing Garlic

I would choose #1, which shows that:

A. My preference for Chocolate > Garlic is significantly stronger than my
preference for Strawberry > Chocolate.
B. If voting honestly, I should give Chocolate at least a 4 out of 5 on a
Score ballot.

The odds can then be varied, to narrow in on a more precise rating, which
is essentially what we all do internally when we rate a movie or restaurant
or product or student or respond to a Likert scale survey, etc.

Of course, this is imprecise, but so is forcing voters to rank many
candidates when they are indifferent between some of them.


If Vanilla and French Vanilla were both on the same ballot, I would be
indifferent between them.  Forcing me to choose between them and then
arbitrarily assigning the same weight to this very weak preference that was
applied to my Chocolate > Garlic preference would be rather undemocratic,

Organisms don't have ordered lists of equal-strength preferences in their
brains.  They have fuzzy estimates of utility that they then convert to
rankings when necessary.

"The majority judgement experiment proves that the model on which the
theory of social choice and voting is based is simply not true: voters do
not have preference lists of candidates in their minds. Moreover, forcing
voters to establish preference lists only leads to inconsistencies,
impossibilities and incompatibilities."

> that tactical question faces the voter in a Score or Approval election the
> second he/she steps into the voting booth.  but not so for the ordinal
> Ranked ballot.

>From what I've been told (though I haven't read and understood it myself),
Gibbard's theorem proves that ALL voting systems require voters to make
tactical decisions, no matter whether they are ranked or rated or otherwise.

On Fri, Jan 10, 2020 at 2:02 AM Rob Lanphier wrote:

> that cardinal voting systems are provably free of any
> sort of impossibility paradox.

I've never heard anyone claim that they are.  The claim is simply that
Arrow's theorem, in particular, doesn't apply to cardinal systems, which
Arrow seems to agree with in that interview (and I don't know why that
would be a big deal or why he shouldn't be trusted to interpret his own
theorem).  Satterthwaite's also doesn't. It's Gibbard's theorem,
specifically, that applies to the general case of all conceivable voting
systems: https://politics.stackexchange.com/a/14245/10373
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20200111/b9725a4c/attachment.html>

More information about the Election-Methods mailing list