[EM] Ranked Preferences, example calculations

[Chris Benham]

Abd ul-Rahman Lomax wrote:

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>>>> The problem with Range is that if  "the majority" are not self-aware
>>>> and coordinated, they cannot
>>>> "easily get what they want".
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>>> On the contrary, the condition being described was that the majority
>>> had a strong preference. Under Range, all they need to do is vote
>>> that preference as a strong one. What coordination does this take?
>>>
>> Again "strong preference" for what exactly?  And how strong is "strong"?
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> The strongest preference is expressed in range by rating the undesired 
> outcome at the minimum rating and the desired outcome at the maximum 
> rating. If the majority does this, and if they are in agreement about 
> these two things, they will prevail.
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> "Strong preference" means strong preference for a desired outcome. If 
> they only have a weak preference, and express such a preference, they 
> might not get it.

CB: This requires them to be coordinated regarding their "desired 
outcome". What if they agree that X should lose but are split about 
which individual candidate should get max. rating,
or  they agree that Y should win but are split about which candidate 
should get minimum rating? Why shouldn't they also "prevail" in those cases?

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>> Range has no real "majority-rule" related guarantees, except a very 
>> unimpressive weakened
>> version of  Minimal Defense that means that for a majority to block 
>> the election of X they
>> must both give X a minimum rating and some other candidate a maximum 
>> rating.
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> Yes. In other words, they express a strong preference.
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>> But since Range is a deterministic method, the lack of guarantees for 
>> the majority necessarily
>> make it vulnerable to strategy.
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> There are value judgements embodied in the language used that 
> essentially incorporate the conclusion.

CB: No, the language is purely technical.

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> He expects that people would engage in a conspiracy to vote 
> insincerely in order to impose their weak preference on the society.
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CB: What "conspiracy"?

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> No, if they are actually going to do this, they have a strong 
> preference. Their so-called "strategic vote" is actually a sincere one.

CB: In my examples, votes that I specify as insincere are insincere.

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> Let's look at what Chris comes up with:
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>> 25001: A99>B98>C0
>> 25000: B99>A98>C0
>> 49999: C99>A0=B0
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> Right off I'll note that these votes are preposterous. People will not 
> vote, in such numbers, anything like this. 

CB: Completely irrelevant for my demonstration.

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>  No election method is going to produce a satisfactory result in this 
> situation. It is entirely unclear to me which of the three candidates 
> is actually the best.
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CB: Of course. With a sincere Majority Loser and a sincere Condorcet 
winner some of us are not so confused.

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> Bottom line, though: if I could make a suggestion to this society, it 
> would be that you need to find a candidate with broader support. Any 
> winner for this election, among the three presented, will result in a 
> badly fractured society, an officer who is *detested* by half the people.

CB: It isn't a "society", it's a hypothetical election profile. I am 
charitably assuming that voters who give their sincere ranking will 
subject to that still try to maximise their clout by voting as close to 
the extremes as possible. If  I didn't do that, then incentives for 
insincere voting in Range would be even more glaring.

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>> Here a majority express the strongest possible preference that C not 
>> win without falsifying their
>> sincere rankings, and yet C wins.  This demonstrates (proves) that 
>> Range fails Majority Loser,
>> Condorcet, Majority for Solid Coalitions and (regular) Minimal Defense.
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>> These failures make Range in this case vulnerable to Compromise 
>> strategy. If  the 2500 B99>
>> A98 voters change to B99=A99, the winner changes from C to A (who 
>> they vastly prefer).
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> Well, I would have to assume that the serious closeness of this 
> election would be known. A shift from 98 to 99 is hardly a major shift.

CB: Sufficient to force those voters to stop expressing their B>A 
preference.

> I've recommended that Range elections include a facility for 
> expressing Favorite *without* giving a higher rating. I've also 
> recommended that Range be coarser, not 0 to 99, I'd rather see 0 to 10.

CB: The fact that the range was so large (99-0) is what forced me to 
make the difference in size between the two factions so small.

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> Now, note that I proposed, in these and concurrent threads, a safety 
> feature, a runoff if the preference winner were different from the 
> Range winner.

CB: Yes *you* did, but that isn't the CRV proposal.  I have been 
addressing the pure Range method, not some as yet not even fully defined 
"Range with Runoff" or "Range with Ratification" scheme of yours.

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>> 25001: A99>B98>C0
>> 25000: B99=A99>C0  (sincere is B>A>>C)
>> 49999: C99>A0=B0
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>> This Abd, is *proof* that Range is vulnerable to the 
>> Compromise(compression) strategy.
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> I don't consider that a vulnerability. Vulnerability implies that 
> there is something wrong with it.

CB: Again, the language is technical.

> Remember, the "sincere" vote here was A99>B98.
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CB: The ranking was sincere but as I explained, the ratings maybe not.

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> This is more interesting:
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>> 36: A99>B98>C0
>> 18: B99>B98>C0
>> 46: C99>A0=B0
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>> This time the AB faction have a comfortable enough majority to win 
>> without insincere equal-ranking, and
>> A (the Condorcet and IRV winner) wins.  But Range (like Approval) is 
>> vulnerable to a form of
>> Burial with a nasty defection incentive.
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>> 36: A99>B98>C0
>> 18: B99>A0=C0   (sincere is B>A>>C)
>> 46: C99>A0=B0
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>> The 18 B voters have "defected" from the AB coalition by insincerely 
>> changing from B99>A98
>> to B99>B0=C0, and Range rewards their dishonesty (and disloyalty) by 
>> electing B.
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> Now, why would they do this? Only if they strongly prefer B to A. But 
> this contradicts the initial conditions.

CB: Range only allows voters to express one "strong" (by your 
definition) preference (between two candidates or two sets of  
equally-ranked candidates). In "the initial conditions"
the B supporters strongest preference was B>C. Of course their sincere 
B>A preference doesn't have to be all that strong for them to want to 
make B win.

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> . And yet we imagine that the B voters are going to lie about their 
> preference, in cahoots with each other, in order to elect B?
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CB: Who (besides you) mentioned anything about them being "in cahoots 
with each other"?  No coordination is needed. As long as the other 
factions vote the same way, individual members of the B faction can try 
the strategy without any risk of it back-firing (and it can work if only 
some of them do it.)

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> The Majority Criterion properly applies (i.e., is desirable) to binary 
> elections. It gets dicey when there are more than two choices.

CB: Why on earth is that, in your book?  "Strength of preference" is 
all-important when there are three candidates, but not two?


Chris Benham

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