[EM] Ordinal voting
Richard Lung
voting at ukscientists.com
Sat Feb 17 09:20:36 PST 2024
I think it would have been more helpful to appreciate that there is no
way round (multiple) order in the vote, whether it be by x-voting, party
voting or cardinal voting, which has the disadvantage of having little
or no usage. (A similar handicap applies to trying to exclude proportion
from the count, without disproportionate results. It is "an exercise in
futility" as Enid Lakeman said of "affirmative gerrymandering.")
As regards x-voting, in the UK, big parties and small parties alike have
been straining, as far back as can be remembered, at least since WW2, to
persuade electors not to elect, but to exclude either small or big
parties. (HG Wells said in 1912, in The Labour Unrest, We no longer have
elections, only Rejections.)
Moving to party voting does not solve the problem. Anika Freden
distinguished four main kinds of strategic voting with party list
systems. What you find in the Cold War divide of elections into Simple
Plurality and Closed Lists, or their amalgamation into a Double X-vote,
is that the voters are denied all but a single-preference X-vote, and
pressured not to waste it on an election!
Elections could not banish ordinal voting but they have turned voting
into a class system of double standards, where contriving politicians
defectively order choices for their leaders, but do not permit a ranked
choice for the general voters.
Cardinal voting confounds an individual vote with a collective count. It
is not for equal voters to say how many votes they think a candidate
should have. That is a collective result of the count. And as Enid
Lakeman said, cumulative votes count against each other.
Richard Lung.
On 17/02/2024 03:47, Closed Limelike Curves wrote:
> First, I'd like to thank Kristofer for his wonderful response+addition
> to this discussion. :-)
>
> I made most of the edits on Wikipedia, and I'm happy to talk about how
> we could try and make them more neutral. My goal wasn't to be a
> cardinal partisan, although I'll admit I'm generally a supporter. I'm
> a big fan of some of the newer Condorcet methods (like Ranked Pairs)
> as well, and I think the difference between these and cardinal methods
> is likely pretty small in practice.
>
> Rather than advocating any particular voting system, my goal was to
> nip some common misunderstandings about these theorems in the bud.
> Mostly these relate to the applicability of some of these theorems
> (especially Arrow's) to cardinal systems. It sounds like in doing so,
> I might have introduced a framing that gives the opposite
> misimpression (that cardinal systems are somehow immune to /any/ kind
> of unpleasant behavior, when they're clearly not).
>
> Here's what I think is important for people to understand on each of
> these topics:
>
> * *Arrow's theorem:* Within the Arrovian paradigm (a function
> aggregates individual preferences to give us social preferences),
> any rule that satisfies IIA (and therefore coherence) is cardinal.
> * *Gibbard-Satterthwaite:* It's impossible to guarantee honesty (no
> preference reversals) for any ordinal voting system with >2
> candidates (original) or any cardinal system with >3 candidates
> (WDS extension).
> o /Comment on semi-honest rankings/: I think honesty in rankings
> and honesty in ratings are both valuable (but distinct)
> notions of honesty, and it's reasonable to separate them.
> Satterthwaite's original theorem focused on ordinal systems,
> however (assuming rankings throughout). Because of that, I
> interpret the theorem as being about ordinal honesty, which
> score voting happens to satisfy for the 3-candidate case.
> o
> /Comment on revelation principle/: You're completely correct.
> I misinterpreted the textbook I've been working from as
> claiming something stronger than it actually was, and I'll fix
> this ASAP.
> * *Gibbard's theorem: *Within the game-theoretic paradigm
> (reported individual preferences are the results of a game, not
> the thing we actually care about), perfect guaranteed honesty is
> impossible for any voting system.
> o /Honest mechanisms: /I do think we want to be clear on the
> distinction between social choice mechanisms and
> voting systems. Some mechanisms (like VCG) can be efficient
> and still guarantee honesty if monetary incentives are available.
>
> By the way, I'd be very interested in a source on strategy implying
> IIA violations, so I can add it to the article!
>
> On Thu, Feb 15, 2024 at 10:00 AM
> <election-methods-request at lists.electorama.com> wrote:
>
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> Today's Topics:
>
> 1. Impossibility on Wikipedia: Arrow, Gibbard, and Satterthwaite
> (Rob Lanphier)
> 2. Re: Impossibility on Wikipedia: Arrow, Gibbard, and
> Satterthwaite (Richard Lung)
> 3. Re: Impossibility on Wikipedia: Arrow, Gibbard, and
> Satterthwaite (Kristofer Munsterhjelm)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 14 Feb 2024 23:13:28 -0800
> From: Rob Lanphier <roblan at gmail.com>
> To: election-methods at lists.electorama.com
> Subject: [EM] Impossibility on Wikipedia: Arrow, Gibbard, and
> Satterthwaite
> Message-ID:
>
> <CAK9hOY=nJQ1QstfHi-6mh42H=_42SPS-Mtqx6r+i-NKueYamTw at mail.gmail.com
> <mailto:42SPS-Mtqx6r%2Bi-NKueYamTw at mail.gmail.com>>
> Content-Type: text/plain; charset="UTF-8"
>
> Hi folks,
>
> I'm going to send a similar email here to the EM list that I recently
> sent to several folks who hang out in academic circles. The answer I
> received from the academic circles was valuable, but I also think that
> folks on this mailing list can provide a different (and useful)
> perspective.
>
> I've long taken it for granted that impossibility theorems like
> Arrow's theorem and Gibbard's theorem mathematically prove that there
> are always going to be important electoral criteria that will be
> mutually exclusive in ANY credible electoral system. I've been at
> peace with that for a long time, much in the same way that I'm at
> peace with mutually exclusive criteria for my transportation needs
> (e.g. I should take something with more carrying capacity than a
> bicycle to go shopping for large furniture, no matter how good the
> bike is). The physics of electoral systems and the physics of the
> real world have certain mathematical rules that are tough to get
> around.
>
> Since the Center for Election Science (<https://electionscience.org>)
> started getting momentum and having some electoral success in the late
> 2010s, there's been a push to distinguish between "cardinal voting"
> and "ordinal voting" as the top of the hierarchy distinguishing all
> voting systems. Since the ballot is what people see, that's
> understandable, I suppose. However, in my mind, the ballots don't
> matter as much as the tallying method, and moreover, it's possible to
> use cardinal voting ballots and then tally them using systems that
> some folks classify as "ordinal" systems.
>
> In discussions with electoral reform folks over the past few years,
> I've been learning about Arrow, Gibbard, and Satterthwaite, and trying
> to document what I've learned on Wikipedia and electowiki.
>
> In editing Wikipedia articles related to election methods in the past
> few years, it seems there are three theorems that have made the rounds
> with regards to impossibility theorems:
>
> 1. Arrow's impossibility theorem (published in 1951): basically the
> granddaddy of impossibility theorems, which seemingly only applies to
> ordinal voting methods.
> <https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem>
> 2. Gibbard's theorem (published in 1973): generalizes Arrow's theorem
> to apply to pretty much every social choice function
> <https://en.wikipedia.org/wiki/Gibbard%27s_theorem>
> 3. The Gibbard?Satterthwaite theorem (published in 1978): a more
> specific version of Gibbard's theorem which apparently only applies to
> ordinal systems, and focuses on strategic voting
> <https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem>
>
> What bothers me of late is a recent change that's been made to the
> Gibbard-Satterthwaite article. I'll quote the most bothersome
> addition/replacement that's in the "Gibbard?Satterthwaite theorem"
> article as of this writing:
> > The theorem does not apply to cardinal voting systems such as score
> > voting or STAR voting, which can often guarantee honest (or
> semi-honest)
> > rankings in cases covered by the Gibbard-Satterthwaite
> theorem,[4] nor
> > does it apply to decision mechanisms other than ranked-choice
> voting.
> > Gibbard's theorem provides a weaker result that applies to such
> > mechanisms.
> >
> > The Gibbard-Satterthwaite theorem is often misunderstood as claiming
> > that "every voting system encourages dishonesty" or the related
> adage
> > that "there is no best voting system." However, such
> interpretations are
> > not correct; by the revelation principle, there exist many
> (deterministic,
> > non-trivial) voting systems that allow for honest disclosure
> (outside the
> > class of ranked-choice voting systems).
>
> It seems disingenuous to say that all of these voting systems don't
> apply to cardinal systems if there is some way to vote "honestly"
> (whatever that means). Strategy and honesty are not mutually
> exclusive, and cardinal systems like "score voting" require voters to
> be very strategic as part of their voting calculus. As noted above,
> Condorcet tallying methods can be used to tally "cardinal ballots" and
> "ordinal ballots", since both express the preferences.
>
> I'll quote what one of the folks in the academic circles stated:
> > Since it seems implausible to suppose that one person?s cardinal
> > evaluations have meaning in comparison to another person?s
> evaluations,
> > it is implausible to suppose that there is such a thing as an
> honest cardinal
> > evaluation of candidates. If there is such a thing as an honest
> cardinal
> > evaluation of candidates, then opportunities to benefit from
> dishonest
> > evaluations of candidates are rife in systems based on cardinal
> > evaluations, while they are likely to be quite rare under Condorcet-
> > consistent ranking-based voting systems.
>
> This assertion more-or-less comports with my opinion. While I don't
> think that systems that insist on ranking-based ballots (ordinal
> ballots) are ALWAYS superior to systems that rely on simple addition
> of rating-based ballots (cardinal ballots), I think the implicit
> rankings are at least as important as the explicit ratings. I
> generally think of STAR voting as "Condorcet lite", because, for two
> finalists "candA" and "candB", the final runoff doesn't pay attention
> to whether:
> scenario 1 ) "candA" has 5 stars and "candB" has 4 stars on ballot
> #1234
> or
> scenario 2) "candA" has 1 star, and "candB" has 0 stars on ballot
> #1234
>
> In the end, in both scenarios, ballot #1234 counts in full for
> "candA", which seems fair to me. Regardless, I've frequently found
> myself distrusting hardcore cardinal advocates when I see changes like
> the one made to English Wikipedia's "Gibbard?Satterthwaite theorem"
> article.
>
> Are cardinal voting advocates correct to continually claim that
> Arrow's, Gibbard's, and Satterthwaite's theorems don't apply to their
> favorite voting methods? Is there a useful distinction to be drawn
> between Gibbard's 1973 theorem and the "Gibbard-Satterthwaite theorem"
> published in 1978? Is the distinction I draw above correct?
>
> Rob
>
>
> ------------------------------
>
> Message: 2
> Date: Thu, 15 Feb 2024 16:02:57 +0000
> From: Richard Lung <voting at ukscientists.com>
> To: Rob Lanphier <roblan at gmail.com>,
> election-methods at lists.electorama.com
> Subject: Re: [EM] Impossibility on Wikipedia: Arrow, Gibbard, and
> Satterthwaite
> Message-ID: <c84dcd1e-0f80-4f4c-920b-c0cf25b4ebb3 at ukscientists.com>
> Content-Type: text/plain; charset=UTF-8; format=flowed
>
>
> Whether you are right or no, there is no conensus on the matter.
> Theorem
> Arrow is like a Cold War between electoral systems. It acknowledges
> ordinal votes as a basis for elections, in a denigratory sort of way,
> but over-looks the count beyond crude plurality. Ever since,
> mathematicians have demonstrated it takes more than mathematics to
> have
> a good understanding of elections. Formerly, it was not so, when they
> acted freely as enthusiasts, but the institutionalisation of election
> studies appears to have robbed them of any independent critical sense.
>
> That understanding, I gather from his parliamentary speeches on "Mr
> Hare's system," is what John Stuart Mill had, the greatest
> philosopher
> of science in the 19th century. The Hare-Mill tradition, that has
> continued to the present day, has been by-passed. In so doing, social
> choice theory reveals its provincialism. A Nobel prize or so, to give
> away, is not a proof. A theorem is only as good as the assumptions on
> which it is based. And theorem Arrow compares to a critique of a
> bicycle
> on the basis of the short-comings of a unicycle. It does not deal
> with
> the democratic necessity of a proportional count as well as an
> ordinal
> vote. Simple plurality is "maiorocracy" or the tyranny of the
> majority,
> as Mill and Lani Guinier said.
>
> It is not apparent what decisive argument the social choice school
> have
> that they can take to the voters, for whom elections are supposed
> to be
> meant, and has not been so for 70 years. It is not even apparent
> that,
> after 70 years, they have any idea of, or even belief in, a standard
> model of democratic election.
>
> Richard Lung.
>
>
> On 15/02/2024 07:13, Rob Lanphier wrote:
> > Hi folks,
> >
> > I'm going to send a similar email here to the EM list that I
> recently
> > sent to several folks who hang out in academic circles. The answer I
> > received from the academic circles was valuable, but I also
> think that
> > folks on this mailing list can provide a different (and useful)
> > perspective.
> >
> > I've long taken it for granted that impossibility theorems like
> > Arrow's theorem and Gibbard's theorem mathematically prove that
> there
> > are always going to be important electoral criteria that will be
> > mutually exclusive in ANY credible electoral system. I've been at
> > peace with that for a long time, much in the same way that I'm at
> > peace with mutually exclusive criteria for my transportation needs
> > (e.g. I should take something with more carrying capacity than a
> > bicycle to go shopping for large furniture, no matter how good the
> > bike is). The physics of electoral systems and the physics of the
> > real world have certain mathematical rules that are tough to get
> > around.
> >
> > Since the Center for Election Science
> (<https://electionscience.org>)
> > started getting momentum and having some electoral success in
> the late
> > 2010s, there's been a push to distinguish between "cardinal voting"
> > and "ordinal voting" as the top of the hierarchy distinguishing all
> > voting systems. Since the ballot is what people see, that's
> > understandable, I suppose. However, in my mind, the ballots don't
> > matter as much as the tallying method, and moreover, it's
> possible to
> > use cardinal voting ballots and then tally them using systems that
> > some folks classify as "ordinal" systems.
> >
> > In discussions with electoral reform folks over the past few years,
> > I've been learning about Arrow, Gibbard, and Satterthwaite, and
> trying
> > to document what I've learned on Wikipedia and electowiki.
> >
> > In editing Wikipedia articles related to election methods in the
> past
> > few years, it seems there are three theorems that have made the
> rounds
> > with regards to impossibility theorems:
> >
> > 1. Arrow's impossibility theorem (published in 1951): basically the
> > granddaddy of impossibility theorems, which seemingly only
> applies to
> > ordinal voting methods.
> > <https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem>
> > 2. Gibbard's theorem (published in 1973): generalizes Arrow's
> theorem
> > to apply to pretty much every social choice function
> > <https://en.wikipedia.org/wiki/Gibbard%27s_theorem>
> > 3. The Gibbard?Satterthwaite theorem (published in 1978): a more
> > specific version of Gibbard's theorem which apparently only
> applies to
> > ordinal systems, and focuses on strategic voting
> >
> <https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem>
> >
> > What bothers me of late is a recent change that's been made to the
> > Gibbard-Satterthwaite article. I'll quote the most bothersome
> > addition/replacement that's in the "Gibbard?Satterthwaite theorem"
> > article as of this writing:
> >> The theorem does not apply to cardinal voting systems such as score
> >> voting or STAR voting, which can often guarantee honest (or
> semi-honest)
> >> rankings in cases covered by the Gibbard-Satterthwaite
> theorem,[4] nor
> >> does it apply to decision mechanisms other than ranked-choice
> voting.
> >> Gibbard's theorem provides a weaker result that applies to such
> >> mechanisms.
> >>
> >> The Gibbard-Satterthwaite theorem is often misunderstood as
> claiming
> >> that "every voting system encourages dishonesty" or the related
> adage
> >> that "there is no best voting system." However, such
> interpretations are
> >> not correct; by the revelation principle, there exist many
> (deterministic,
> >> non-trivial) voting systems that allow for honest disclosure
> (outside the
> >> class of ranked-choice voting systems).
> > It seems disingenuous to say that all of these voting systems don't
> > apply to cardinal systems if there is some way to vote "honestly"
> > (whatever that means). Strategy and honesty are not mutually
> > exclusive, and cardinal systems like "score voting" require
> voters to
> > be very strategic as part of their voting calculus. As noted above,
> > Condorcet tallying methods can be used to tally "cardinal
> ballots" and
> > "ordinal ballots", since both express the preferences.
> >
> > I'll quote what one of the folks in the academic circles stated:
> >> Since it seems implausible to suppose that one person?s cardinal
> >> evaluations have meaning in comparison to another person?s
> evaluations,
> >> it is implausible to suppose that there is such a thing as an
> honest cardinal
> >> evaluation of candidates. If there is such a thing as an honest
> cardinal
> >> evaluation of candidates, then opportunities to benefit from
> dishonest
> >> evaluations of candidates are rife in systems based on cardinal
> >> evaluations, while they are likely to be quite rare under
> Condorcet-
> >> consistent ranking-based voting systems.
> > This assertion more-or-less comports with my opinion. While I don't
> > think that systems that insist on ranking-based ballots (ordinal
> > ballots) are ALWAYS superior to systems that rely on simple addition
> > of rating-based ballots (cardinal ballots), I think the implicit
> > rankings are at least as important as the explicit ratings. I
> > generally think of STAR voting as "Condorcet lite", because, for two
> > finalists "candA" and "candB", the final runoff doesn't pay
> attention
> > to whether:
> > scenario 1 ) "candA" has 5 stars and "candB" has 4 stars on
> ballot #1234
> > or
> > scenario 2) "candA" has 1 star, and "candB" has 0 stars on
> ballot #1234
> >
> > In the end, in both scenarios, ballot #1234 counts in full for
> > "candA", which seems fair to me. Regardless, I've frequently found
> > myself distrusting hardcore cardinal advocates when I see
> changes like
> > the one made to English Wikipedia's "Gibbard?Satterthwaite theorem"
> > article.
> >
> > Are cardinal voting advocates correct to continually claim that
> > Arrow's, Gibbard's, and Satterthwaite's theorems don't apply to
> their
> > favorite voting methods? Is there a useful distinction to be drawn
> > between Gibbard's 1973 theorem and the "Gibbard-Satterthwaite
> theorem"
> > published in 1978? Is the distinction I draw above correct?
> >
> > Rob
> > ----
> > Election-Methods mailing list - see https://electorama.com/em
> for list info
>
>
> ------------------------------
>
> Message: 3
> Date: Thu, 15 Feb 2024 18:48:22 +0100
> From: Kristofer Munsterhjelm <km_elmet at t-online.de>
> To: Rob Lanphier <roblan at gmail.com>,
> election-methods at lists.electorama.com
> Subject: Re: [EM] Impossibility on Wikipedia: Arrow, Gibbard, and
> Satterthwaite
> Message-ID: <3a9c9f20-0d6f-0206-bb48-10b5f335ea9d at t-online.de>
> Content-Type: text/plain; charset=UTF-8; format=flowed
>
> On 2024-02-15 08:13, Rob Lanphier wrote:
> > Hi folks,
> >
>
> > Are cardinal voting advocates correct to continually claim that
> > Arrow's, Gibbard's, and Satterthwaite's theorems don't apply to
> their
> > favorite voting methods? Is there a useful distinction to be drawn
> > between Gibbard's 1973 theorem and the "Gibbard-Satterthwaite
> theorem"
> > published in 1978? Is the distinction I draw above correct?
>
> My understanding and opinion is this:
>
> You have three different "main" impossibility theorems:
>
> - Arrow's says that no deterministic reasonable ordinal voting method
> can pass IIA. This means that regardless of whether voters are
> honest or
> strategic, it's possible that A's win over B depends on not just how
> many voters prefer A to B, but also how many prefer X to Y. This
> is only
> for cardinal methods.
>
> - Gibbard-Satterthwaite says that no deterministic reasonable ordinal
> method is strategy-proof: there always exists at least one election
> where at least one voter has an incentive to adjust his preferences
> based on how others are voting.
>
> - Gibbard's theorem extends this to a much broader class of election
> methods that includes cardinal methods, thus also implying that no
> deterministic cardinal voting method is strategy-proof.
>
> (In particular, both of Gibbard's theorems are about strategy.)
>
> The part about the revelation principle is incorrect and seems to be
> using a very specific definition of honesty, inspired by Warren
> Smith.
> To my knowledge, what the revelation principle says is this:
>
> - Say that a participant in a mechanism employs strategy if the
> information he submits to the mechanism depends on the actions of the
> other participants or his belief about them.[1]
>
> - Say that a mechanism only uses honesty if no participant has an
> incentive to employ strategy.
>
> - Then, if there exists a mechanism where people employ strategy to
> drive it to an optimal or equilibrium outcome, then there also
> exists a
> mechanism that only uses honesty that reaches the same outcome or
> equilibrium.
>
> Consider it like this: suppose you're involved in a court case,
> and you
> hire a lawyer. You tell the lawyer the truth and the lawyer comes up
> with whatever strategy that will advance your interests, given the
> evidence and information about the other party. That's a system where
> you or your lawyer use strategy to drive the system to a
> particular state.
>
> But consider a hypothetical legal system using an AI judge. This
> AI has
> a lawyer interface to each party; upon hearing the truth from each
> party, it then simulates a court case the way it would proceed with
> virtual lawyers who employs strategy based on the honest information.
> The AI comes with a proof that your virtual lawyer won't incriminate
> you. You would then interact honestly with the system, represented by
> the judge, and it would strategize internally.
>
> Thus for any system that requires strategy to get an equilibrium,
> there
> exists another system where you can be honest. It just absorbs the
> "lawyer component" into itself.
>
> The problem is that there is no such equilibrium for deterministic
> voting methods. That's implied by Gibbard, because otherwise, you
> could
> create a strategy-proof method by first creating a method that
> invites a
> particular type of strategy, and then embodying a "lawyer component"
> into it to perform that strategy.
>
> If you try to do this, as far as I understand it, you get a
> nondeterministic method since the equilibrium is a mixed strategy.
> And,
> as we know, there exist strategy-proof nondeterministic methods,
> so that
> fits.
>
> This would be like: sometimes, your lawyer says "if we do this,
> then no
> matter what the other party does, we win". But other times he says
> "if
> we focus on these elements and the other party focuses on those,
> then we
> win". Like rock-paper-scissors, which strategy you should play
> depends
> on the strategy the other guy is going to use. So you play them at
> random in such a way that the other guy can't guess what you're
> doing.
> That gives a nondeterministic method.
>
> Okay.
>
> So now about IIA.
>
> The seeming advantage that cardinal methods have over ordinal ones is
> that they pass IIA. In Range, if A has score 100 and B has score 50,
> then A will continue to beat B even if we remove every other
> candidate.
>
> But I've always been of the opinion that this IIA compliance is
> either
> illusory or a distraction, because it doesn't answer what we
> really care
> about. And that is whether the presence of a candidate who doesn't
> win
> changes the outcome.
>
> Some cardinal proponents say that methods like Range have multiple
> honest ballots: there are many ways to vote that are all
> consistent with
> your preference ordering. But a voter has to choose which honest
> ballot
> to cast, and there's no externally fixed scale (what exactly does ten
> points mean? What does zero mean?).[2] Thus the selection of
> candidates
> who run will affect the scale, which means that some voters would
> change
> their ratings based on who's running - even if those additional
> candidates don't win. So these methods fail what we could call "de
> facto
> IIA", for lack of a better term.
>
> For instance, suppose the election starts off with two pro-democracy
> candidates. Then a number of authoritarians enter the race. It's
> likely
> that in Approval, some voters who would've approved of one of the
> pro-democracy candidates but not the other, would now approve both to
> mark their distaste for authoritarianism and keep the authoritarians
> from winning.
>
> So in my opinion, ordinal methods are merely honest about their
> limitations. Their logic says: "okay, I can't know if his 10/10 is
> the
> same as her 10/10 or her 5/10. I'll accept that this means I must
> fail
> IIA, instead of seeming to pass it by passing the buck to the voters
> that they must use a fixed scale that's not affected by who's in
> the race."
>
> So ordinal methods clearly fail IIA, and aren't strategy-proof (by
> Gibbard-Satterthwaite). Cardinal methods pass IIA (but it doesn't
> mean
> what one may think it means) and aren't strategy-proof (by Gibbard's
> theorem).
>
> Both ordinal and cardinal methods may pass de facto IIA for
> subsets of
> elections. E.g. Condorcet methods pass IIA as long as there is a CW,
> because adding a candidate either makes that candidate the new CW
> (hence
> he's not irrelevant) or the current winner stays a CW. Similarly,
> Approval passes de facto IIA with dichotomous preferences where every
> voter has a class of OK candidates and a class of not-OK
> candidates, and
> the boundary between OK and not OK doesn't depend on who's in the
> race.
> (Such voters may sometimes approve everybody or nobody.)
>
> But in general: both cardinal and ordinal methods are susceptible to
> strategy. And both cardinal and ordinal methods may have the winner
> change from A to B as a consequence of C entering the race.
>
> -km
>
> [1] Strictly speaking we would also want "honesty" to have some
> connotation of "being the actual information being asked for". Say
> you're dealing with a system that asks you what you like the least
> and
> then gives it to you. You would answer its question with a thing that
> you want to be given, so that answer stays the same no matter what
> other
> people interacting with it would say. So by my definition that
> wouldn't
> be strategy, but common-sense would say that it is not honest either.
>
> Warren's definition of honesty is somewhat based on this idea, but it
> goes too far in the other direction. It doesn't consider ballots
> where
> your ranking stays the same as under honesty but your scores
> don't, as
> being strategic. I think in part that's due to the difficulty in
> comparing utilities, but we *can* hold rated voting to a higher
> standard. Ask and I'll elaborate - this post is long enough :-)
>
> [2] As a side note: we probably can make *some* observations of other
> people's utilities even if we don't have a fixed scale. For
> instance, I
> can probably reason that a candidate who would put you in a prison
> camp
> would be a much worse choice from your perspective than one who would
> arrange a party; and that the difference in utilities would be much
> greater than say, between a candidate who holds a week-long party and
> one who holds a two-week long party.
>
> Some cardinal proponents also refer to von Neumann-Morgenstern
> utilities
> as a way of making comparisons between people's strength of
> preference:
> basically using lotteries to determine how much more a voter
> prefers one
> choice to another. But such scales still need to be normalized
> because
> they always have two unknown variables per voter. Methods that do the
> normalization so as to give each voter the same strength fail IIA.
> Not
> doing such renormalization can make the method pass IIA but they
> still
> don't pass "de facto IIA".
>
> See e.g.
> https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem#Incomparability_between_agents
>
> for the need for normalization.
>
>
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>
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> ------------------------------
>
> End of Election-Methods Digest, Vol 235, Issue 30
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