[EM] Expressing pairwise preferences

[Dave Ketchum]

On Sun, 14 Aug 2005 01:11:32 +0300 Juho Laatu wrote:

> Hi Dave,
> 
> I think I agree with you on that in normal elections (e.g. presidential 
> elections) and for normal voters the described additional voting options 


Generally best to ignore US presidential elections, unless your topic 
includes some of their peculiarities, such as the electoral college.

Governor and mayoral elections are usually a better topic identifier for 
electing a single winner.

> are not needed and probably even harmful. The standard rules (of 
> allowing voters to give one linear list of candidates, maybe allowing 
> equal ranking, ranking unlisted candidates as last, and deriving 
> transitive preferences from the vote) are in most cases a very 
> understandable and sufficiently expressive way to describe the opinions 
> of the voters. My intention was to demonstrate that in most practical 
> cases the current default rules are the best rules (although one could 
> consider some additions in some very special elections).


Question possibility of finding a special election deserving "some additions".

> 
> I also embedded some responses to your questions in the mail below.
> 
> BR, Juho
> 
> 
> On Aug 13, 2005, at 20:46, Dave Ketchum wrote:
> 
>> Thanks to Juho for discussing some details.
>>
>> While there have to be voters who would be tempted by each, if 
>> available, they share a serious problem, and I will comment on each 
>> below.  They complicate the rules:
>>      Voters must understand what is permitted, and what each facility 
>> means.
>>      Vote counters must have the same, unambiguous, understanding of 
>> the meaning of each.
>>
>> On Sat, 13 Aug 2005 12:52:32 +0300 Juho Laatu wrote:
>>
>>> Hello Dave et al,
>>> On Aug 13, 2005, at 06:16, Dave Ketchum wrote:
>>>
>>>> I __do__ get to express my n x (n-1) / 2 pairwise preferences (part 
>>>> or all, as I as a voter choose).  I just am forced to be consistent. 
>>>>  If I vote A>B and B>Z, then I have voted A>Z.  If there is a C for 
>>>> which I have given no explicit specification, then my above partial 
>>>> vote implies A>C, B>C, and Z>C.
>>>
>>
>> I would add to the above ability to vote A=D.  Relative to other 
>> candidates it has the same meaning as voting the pair A>D or D>A.  In 
>> counting, two voters voting A=D has the same effect as one voting A>D 
>> and one D>A - matters in wv; does not matter in margins.
>>
>>> Few observations about the ability to express the n x (n-1) / 2 
>>> preferences:
>>> 1) It would be quite easy to remove the rule of considering unranked 
>>> candidates to be ranked last. This could of course lead to unwanted 
>>> results like the most unknown and uninteresting candidate winning the 
>>> election. For this reason it is good that by default 
>>> unranked(/unknown) candidates are considered to be less preferred 
>>> than the ranked ones. In principle it would be ok to allow those 
>>> voters that know what they are doing to express their opinions also 
>>> more widely, e.g. a>b>c[cut] (which means that unlisted candidates 
>>> are not ranked last) or
>>
>>
>>
>> How else would you count an unranked candidate?
> 
> 
> I was thinking of two options. In a four candidate race vote "a>b>c" (d 
> is unranked) would be counted either as a>b, a>c, a>d, b>c, b>d, c>d or 
> as a>b, a>c, a>d.
> 

Not clear.  The string that includes "c>d" is exactly what I expect for 
considering d to be ranked last.

The other string looks incomplete.

>>
>>> 2) a>b>others>c. The latter option introduces the risk of people 
>>> ranking widely the strongest competitors of their favourite candidate 
>>> last, even though that normally doesn't do them much good (would e.g. 
>>> lead to election of some unknown candidate in the case of three major 
>>> candidates).
>>
>>
>>
>> This reads as doable - is it desirable enough to be worth the effort?  
>> I dislike it, liking better leaving at the bottom all those not worth 
>> mentioning (those worth mentioning as better than C are already 
>> votable as such).
>>
>>> 3) It would be also possible to allow circular rankings like a>b>c>a 
>>> (mentioning "a" twice means that the intention is to describe a 
>>> loop). Consistent voters do not normally have such looped opinions I 
>>> guess, but they could be used for strategic or counter strategic 
>>> reasons. (I don't however want to encourage this kind of voting since 
>>> I think that voting methods that use strategies and counter 
>>> strategies extensively are most probably not good enough to be used 
>>> in normal public elections anyway.)
>>
>>
>>
>> Again, how do you count such a vote - assuming you claim it should 
>> have meaning when counting)?
> 
> 
> Yes, counting the votes gets more tricky. I think one natural counting 
> method would be to forget transitive preferences in a loop. Vote 
> "a>b>c>d>a" would then mean a>b, b>c, c>d, d>a, but not e.g. a>c. 
> (Alternatively one could derive also a>c, a>d, b>d from the example vote 
> above.) Unranked candidates (e) could be counted as usual => a>e, b>e, 
> c>e, d>e.


Not clear to me.

> 
> (Sorry about using the ">" relation in two ways above, both in the 
> ballots and when describing which matrix entries get the points.)
> 
>>
>> Of course, groups of voters can, together, create a cycle that the 
>> counters must break - by deciding which leg of the cycle is weakest - 
>> but there is no weakest leg if/when a single voter is allowed to do this.
>>
>>> 4) One option would be to allow candidates to be grouped. This could 
>>> be useful if the number of candidates is large. One could vote for 
>>> example Bush>Gore>Reagan>Republicans>Democrats>Greens ("Republicans" 
>>> will be interpreted here as "other Republican candidates than Bush 
>>> and Reagan" etc.).
>>
>>
>>
>> Reads as doable.  Desirable to encourage this type of thinking?
> 
> 
> Not desirable if one can live without such markings. Some people may 
> also dislike the introduction of parties in general. As I wrote, in 
> situations where the number of candidates is very large (= too tedious 
> to list them all) and natural groupings exist this type of markings 
> could help the voters a bit. Can't however think of any good real life 
> examples at the moment.
> 

I dislike on principle - we should have emphasis on individual candidates.
      Lack of need - not often do we have so many candidates which voters 
cannot dispose of easily via truncation.

>>
>>> Allowing individual Republican candidates to be ranked below the 
>>> generic "Republicans" item could be banned even if such use of group 
>>> entries would be allowed otherwise. This is to avoid the negative 
>>> effects discussed in case 2. It may be better to force voters to list 
>>> all republican candidates if they want to place one of them last. In 
>>> this way they are at least forced to see what kind of (maybe even 
>>> less wanted and totally unknown) candidates they are ranking above 
>>> the candidate they want to rank last, and probability of "unintended 
>>> stupid votes" would probably decrease.
>>
>>
>>
>> Reads as doable.  Sales pitch above sounds deservedly weak.
>>
>>> 5) Yet another way of voting would be to use fragmented votes. One 
>>> could vote Bush>Reagan;Gore>Clinton, which means that Bush is 
>>> preferred to Reagan and Gore is preferred to Clinton but the voter 
>>> has not indicated anything about if (s)he prefers Bush to Gore or the 
>>> other way around, Bush to Clinton etc. I think voters that would be 
>>> interested in voting this way would still be quite consistent. It is 
>>> quite ok to have an opinion "Bush is nicer than Reagan but I don't 
>>> care if Republicans or Democrats will win (others may decide)".
>>
>>
>>
>> Voters might dream they are being consistent.  WHAT have they said to 
>> the counters?
> 
> 
> I think the semicolon was enough in the vote "Bush>Reagan;Gore>Clinton". 
> The vote should be read pretty much like two separate votes 
> "Bush>Reagan" and "Gore>Clinton" (of course counting must be done so 
> that one voter can not add several points to one matrix entry by e.g. 
> voting "a>b;a>b;a>b;a>b"). Did I answer your question?
> 

Agreed that the semicolon is a usable way for the voter to say this.

I was asking what meaning it should have to the voter and the counter. 
The counter needs to extract whatever meaning exists in deciding Bush vs Gore.

>>
>>> The current (EM) default rules concerning ranking based ballots are 
>>> simple, in most cases they offer voters all the tools they need, and 
>>> they often stop voters making foolish things (like ranking their 
>>> worst enemies last or electing some unknown candidates). It could be 
>>> possible to allow e.g. some or all of the five special cases above to 
>>> be used but I doubt if they would bring more benefits than they do 
>>> bring problems in the form of making the system more complex and 
>>> inviting voters to do something stupid. Case 4 could maybe be helpful 
>>> if the number of candidates is large. I have also sometimes had 
>>> feelings like the example in case 5 myself. Note that combination of 
>>> cases 5 and 1 makes it possible to set separately any of the n x 
>>> (n-1) / 2 pairwise preferences.
>>> Best Regards,
>>> Juho

-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
                  If you want peace, work for justice.