[EM] High Resolution Inferred Approval version of ASM

John john.r.moser at gmail.com
Fri Jun 21 16:58:53 PDT 2019 

Hah.  I should have researched more.

It turns out online reviews are superior to a coin flip at most 20% of the
time.  With a 2-star difference, a coin flip will pick the superior product
50% of the time, but the reviews might favor the better product as much as
70% of the time.  That means you'll get 20% more outcomes selecting the
better product from using the reviews than you will by flipping a coin to
decide between a 5-star product and a 3-star product.

Yes, that means cardinal rating reviews are kind of useless about 80% of
the time, as people have trouble determining precisely how good or bad
something is—although given two alternatives, they're really good at
identifying the better one.

[image: image.png]

On Fri, Jun 21, 2019 at 7:48 PM John <john.r.moser at gmail.com> wrote:

> Also it's well-understood ratings are of poor quality in online reviews.
> There is a lot of research into how people overemphasize bad experiences as
> low ratings, and give inflated good ratings.  A lot of products have more 5
> and 1 star ratings than 3 star ratings.
>
> That's not the same thing as comparatively scaling things, which is even
> harder.  There's a reason we have a lot of top 10 lists and a lot of
> rankings for things.
>
> On Fri, Jun 21, 2019, 7:45 PM John <john.r.moser at gmail.com> wrote:
>
>> The error comes when you make inferences.
>>
>> The great purported benefit of score systems is that more voters can rank
>> A over B, yet due to the scores score can elect B:
>>
>> A:1.0 B:0.9 C:0.1
>> C:1.0 A:0.5 B:0.4
>> B:1.0 A:0.2 C:0.1
>>
>> A=1.7, B=2.3, C=2.2
>>
>> Both B and C defeat A, despite A defeating both ranked.
>>
>> If the first voter scores B as 0.7, C wins.
>>
>> Whenever a system attempts to use score or its low-resolution Approval
>> variant, it is relying on this information.
>>
>> So why does this matter?
>>
>> The voters are 100% certain and precise that these are their votes:
>>
>> A>B>C
>> C>A>B
>> B>A>C
>>
>> We know A defeats B, A defeats C, and B defeats C.  A is the Condorcet
>> winner.
>>
>> For score votes, 1.0 is always 1.0.  It's the first rank, the measure.
>> This is of course another source of information distortion in cardinal
>> systems: how is the information meaningful as a comparison between two
>> voters?
>>
>> How do you know 10 voters voting A first at 1.0 aren't half as invested
>> in A as 6 voters voting B 1.0, this really A=5 B=6?
>>
>> Ten of us prefer strawberry to peanut butter.
>>
>> Six of us WILL DIE IF YOU OPEN A JAR OF PEANUT BUTTER HERE.
>>
>> Score systems claim to represent this and capture this information, but
>> they can't.
>>
>> (Notice I used the negative: that 1.0 vote is an expression of the damage
>> of their 0.0-scored alternative.)
>>
>> Even setting that aside, however, you have a problem where an individual
>> might put down 0.7 or 0.9 or 0.5 for the SAME candidate in the SAME
>> election, solely based on how bad they are at creating a cardinal
>> comparison.  Humans are universally bad at cardinal comparison.
>>
>> So now you can actually elect A, B, or C based on how well-rested people
>> are, how hungry they are, or anything else that impacts their mood and thus
>> the sharpness or softness by which they critically compare candidates.
>>
>> It's a sort of random number generator.
>>
>> Wrapping it in a better system and using that information to make
>> auxiliary decisions is still incorporating bad data.  Bad data is worse
>> than no data.
>>
>> On Fri, Jun 21, 2019, 7:27 PM Felix Sargent <felix.sargent at gmail.com>
>> wrote:
>>
>>> I don't know how you can think that blurrier data would end up with a
>>> more precise result.
>>> No matter how you cut it, if you rank ABCD then it translates into a
>>> score of
>>> A: 1.0
>>> B: .75
>>> C: 0.5
>>> D: 0.25
>>>
>>> There's no way of describing differences between candidates beyond a
>>> straight line between first place and last place.
>>> Even if the voter is imprecise in the difference between A and B they
>>> will never make the error of rating B more than A, whereas the error
>>> between a voter's actual preferences and the preferences that are recorded
>>> with an ordinal ballot has the liability of being massive. Consider I like
>>> A and B but HATE C. ABC does not tell you that.
>>> That's not even going into what happens when a voter ranks an ordinal
>>> ballot strategically, placing "guaranteed losers" to 2nd and 3rd places in
>>> order to improve the chances of their first choice candidate (in IRV at
>>> least).
>>>
>>> Your analysis depends on the question of how intelligent you believe the
>>> average voter to be.
>>> If voters can use Amazon and Yelp star ratings, they can do score voting.
>>>
>>> Felix Sargent <https://felixsargent.com>
>>>
>>>
>>>
>>> On Fri, Jun 21, 2019 at 2:14 PM John <john.r.moser at gmail.com> wrote:
>>>
>>>> Cardinal voting collects higher-resolution data, but not necessarily
>>>> precise data.
>>>>
>>>> Let's say you score candidates:
>>>>
>>>> A: 1.0
>>>> B: 0.5
>>>> C: 0.25
>>>> D: 0.1
>>>>
>>>> In reality, B is 90% as favored as A. C is 70% as favored as B.  The
>>>> real numbers would be:
>>>>
>>>> A: 1.0
>>>> B: 0.9
>>>> C: 0.63
>>>> D: etc.
>>>>
>>>> How would this happen?
>>>>
>>>> Cardinal: I approve of A 90% as much as B.
>>>>
>>>> Natural and honest: I prefer A to win, and I am not just as happy with
>>>> B winning, or close to it.  I feel maybe half as good about that?  B is
>>>> between C and D and I don't like C, but I like D less.
>>>>
>>>> Strategic: even voting 0.5 for B means possibly helping B beat A, but
>>>> what if C wins...
>>>>
>>>> The strategic nightmare is inherent to score and approval systems.
>>>> When approvals aren't used to elect but only for data, people are not
>>>> naturally inclined to analyze a score representing their actual approval.
>>>>
>>>> Why?
>>>>
>>>> Because people decide by simulation. Simulation of ordinal preference
>>>> is easy: I like A over B.  Even then, sometimes you can't seem to decide
>>>> who is better.
>>>>
>>>> Working out precisely how much I approve of A versus B is harder.  It
>>>> takes a lot of effort and the basic simulation approach responds heavily to
>>>> how good you feel about A losing to B, not about how much B satisfies you
>>>> on a scale of 0 to A.
>>>>
>>>> Score and approval voting source a high-error, low-confidence sample.
>>>> It's like recording climate data by licking your finger and holding it in
>>>> the wind each day, then writing down what you think is the temperature.
>>>> Someone will say, "it's more data than warmer/colder trends!" While
>>>> ignoring that you are not Mercury in a graduated cylinder.
>>>>
>>>>
>>>> On Fri, Jun 21, 2019, 3:10 PM Felix Sargent <felix.sargent at gmail.com>
>>>> wrote:
>>>>
>>>>> Valuation can be ordinal, in that you can know that 3 is more than 2.
>>>>> There are two questions before us: Which voting method collects more
>>>>> data? Which tabulation method picks the best winner from that data?
>>>>>
>>>>> Which voting method collects more data?
>>>>> Cardinal voting collects higher resolution data than ordinal voting.
>>>>> Consider this thought experiment. If I give you a rating of A:5 B:2 C:1 D:3
>>>>> E:5 F:2 you should create an ordered list from that -- AEDFBC. If I gave
>>>>> you AEDFBC you couldn't convert that back into its cardinal data.
>>>>>
>>>>> Which tabulation picks a better winner from the data?
>>>>> Both Score and Approval voting pick the person with the highest votes.
>>>>> Summing ordinal data, on the other hand, is very complicated, as to
>>>>> avoid loops. Methods like Condorcet or IRV have been proposed to eliminate
>>>>> those but ultimately they're hacks for dealing with incomplete information.
>>>>>
>>>>> Felix Sargent <https://felixsargent.com>
>>>>>
>>>>>
>>>>>
>>>>> On Fri, Jun 21, 2019 at 5:23 AM John <john.r.moser at gmail.com> wrote:
>>>>>
>>>>>> Voters can't readily provide meaningful information as score voting.
>>>>>> It's highly-strategic and the comparison of cardinal values is not natural.
>>>>>>
>>>>>> All valuation is ordinal.  Prices are based from cost; but what
>>>>>> people WILL pay, given no option to pay less, is based on ordinal
>>>>>> comparison.
>>>>>>
>>>>>> Is X worth 2 Y?
>>>>>>
>>>>>> For the $1,000 iPhone I could have a OnePlus 6t and a Chromebook.
>>>>>> The 6t...I can get a cheaper smartphone, but I prefer the 6t to that phone
>>>>>> plus whatever else I buy.
>>>>>>
>>>>>> I have a higher paying job, so each dollar is worth fewer hours, so
>>>>>> the ordinal value of a dollar to me is lower.  $600 of my dollars is
>>>>>> fewer hours than $600 minimum wage dollars.  I have access to my
>>>>>> most-preferred purchases and can buy way down into my less-preferred
>>>>>> purchases.
>>>>>>
>>>>>> Information about this is difficult to pin down by voter.  Prices in
>>>>>> the stock market set by a constant, public auction among millions of buyers
>>>>>> and sellers.  A single buyer can hardly price one stock against another,
>>>>>> and prices against what they think their gains will be relative to current
>>>>>> price.
>>>>>>
>>>>>> When pricing candidates, you'll see a lot like Mohs hardness: 2 is
>>>>>> 200, 3 is 500, 4 is 1,500; but we label things that are 250 or 450 as 2.5,
>>>>>> likewise between 500 and 1,500 is 3.5.  Being between X and Y is always
>>>>>> immediately HALFWAY between X and Y, most intuitively.
>>>>>>
>>>>>> The rated system sucks even before you factor in strategic concerns
>>>>>> (which only matter if actually using a score-driven method).
>>>>>>
>>>>>> Approval is just low-resolution (1 bit) score voting.
>>>>>>
>>>>>> On Fri, Jun 21, 2019, 12:01 AM C.Benham <cbenham at adam.com.au> wrote:
>>>>>>
>>>>>>> Forest,
>>>>>>>
>>>>>>> With paper and pencil ballots and the voters only writing in their
>>>>>>> numerical scores it probably isn't very practical for the Australian
>>>>>>> Electoral Commission
>>>>>>> hand vote-counters.
>>>>>>>
>>>>>>> But if it isn't compulsory to mark each candidate and the default
>>>>>>> score is zero, I'm sure the voters could quickly adapt.
>>>>>>>
>>>>>>> In the US I gather that there is at least one reform proposal to use
>>>>>>> these type of ballots. One of these, "Score Voting" aka "Range Voting",
>>>>>>> proposes to just use Average Ratings with I gather the default score
>>>>>>> being "no opinion"  rather than zero and some tweak to prevent an unknown
>>>>>>> candidate from winning.
>>>>>>>
>>>>>>> So it struck me that if we can collect such a large amount of
>>>>>>> detailed information from the voters then we could do a lot more with it,
>>>>>>> and if we
>>>>>>> want something that meets the Condorcet criterion this is my
>>>>>>> suggestion.
>>>>>>>
>>>>>>> Chris Benham
>>>>>>>
>>>>>>> https://rangevoting.org/
>>>>>>>
>>>>>>> *How score voting works:*
>>>>>>>
>>>>>>>    1. Each vote <https://rangevoting.org/MeaningOfVote.html> consists
>>>>>>>    of a numerical score within some range (say 0 to 99
>>>>>>>    <https://rangevoting.org/Why99.html>) for each candidate.
>>>>>>>    Simpler is 0 to 9 ("single digit score voting").
>>>>>>>
>>>>>>>
>>>>>>> On 21/06/2019 5:33 am, Forest Simmons wrote:
>>>>>>>
>>>>>>> Chris, I like it especially the part about naive voters voting
>>>>>>> sincerely being at no appreciable disadvantage while resisting burial and
>>>>>>> complying with  the CD criterion.
>>>>>>>
>>>>>>> From your experience in Australia where full rankings are required
>>>>>>> (as I understand it) what do you think about the practicality of rating on
>>>>>>> a scale of zero to 99, as compared with ranking a long list of candidates?
>>>>>>> Is it a big obstacle?
>>>>>>>
>>>>>>>
>>>>>>>
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