[EM] Expressing pairwise preferences

[Juho Laatu]

See my comments in the mail below.

BR, Juho


On Aug 14, 2005, at 05:57, Dave Ketchum wrote:

> 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.

Ok. Maybe the default setting for Condorcet elections in this mailing 
list is: single winner election for for regular people (=that are not 
EM experts) where number of voters is large (=large enough to avoid 
analysing votes one by one), candidates are not specifically tied to 
the background political structure(*), number of candidates is quite 
small (typically less than 10). Some countries have presidents, some 
don't. Some countries vote for governors and mayors, some don't.

(*) With "specifically tied to the background political structure" I 
refer e.g. to the US presidential elections that have some interesting 
features. The two-party system makes of course two of the candidates 
major candidates by default. The US presidential election also leads to 
changing many people in the offices of Washington. Condorcet method 
could in principle elect a US president that is a centrist compromise 
candidate between the two major parties, that would be a Condorcet 
winner, but that gets no votes that rank the president first (see 
example below). Whom would the president appoint as the secretary of 
state etc. if (s)he has only Republican and Democrat first place 
supporters around (well, I guess there would be volunteers :-). The 
point anyway is that US presidential elections are not just about 
electing the most appropriate "single" winner but one expects the 
elected person to have heavy support from a large machinery, capable of 
rearranging Washington. This of course makes independent candidates 
less credible.

34: A>D>B>C
33: B>D>C>A
33: C>D>A>B

>
>> 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 too have difficulties in finding credible examples. Maybe the best 
one I found was an election with more than 100 candidates, no clear 
leading candidates, in a multiparty country, most candidates linked to 
the parties. => Ability to use generic names referring to 
groupings/parties (option 4) would make voting easier and results more 
sensible (less random).

>
>> 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.

Sorry, I had a typo there. The second set should be a>b, a>c, b>c. 
Candidate "d" thus will not get any points (for or against).

>
>>>
>>>> 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.

I'll explain my problem/solutions in other words. If there is a loop 
a>b>c>d>a, based on our normal way of reading votes one can derive also 
preference a>c from that vote. The loop could however be expressed also 
in another way: b>c>d>a>b. Now we could derive c>a from the latter 
vote. This contradicts the first (a>c) conclusion. Are a>b>c>d>a and 
b>c>d>a>b similar votes or not? My first interpretation was that they 
are, and I could not derive a>c nor c>a from the (looped parts of the) 
ballots. My second interpretation was that the order in which the loop 
has been written down has a meaning, and then I could derive transitive 
preferences like a>c if the letters "a" and "c" occur in that order 
(from left to right) (with explicit or implicit ">" sign somewhere 
between them) in the ballot.

>
>> (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 counter would fill the matrix as follows. (S)he starts with Bush. 
One point will be added in the matrix for B>R, then one point for B>X 
for all X that is a candidate that is not ranked in this ballot (i.e. 
someone else than B, R, G, C). Then one adds R>X for all unranked X. 
Then G>C, and G>X for all unranked X. And finally C>X for all unranked 
X. Bush vs. Gore result was thus 0-0 in this ballot. (same result for 
B-C, R-G and R-C)

>
>>>
>>>> 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.
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>