(1) Philosophy of interests (introduction)
E.g. using foods (instead of candidates):
- there are foods that you are willing to eat (make you happy, satisfied), foods that you are not willing to eat (make you sad, unsatisfied) and unknown foods → Categories: Positive, Negative, Unknown
- Among the positive and negative foods, however, there may be some more positive than others → Sorting .
- In addition to sorting, it’s also important how much better or worse one food is → Distance .
- Unknown foods are (statistically) better than negative ones and worse than positive ones.
The real interests of a voter will take a numerical form similar to this, with range [-10,10]:
10 7 6 5 1 0 -2 -4 -8 -9 -10
0: for unknown candidates.
(0,10]: for positive candidates.
[-10,0): for negative candidates.
(2) Form of the vote
Hypothesis of voter real interests:
10 8 6 4 2 0 -2 -4 -6 -8 -10
Honest voting can take 4 forms:
10 9 8 7 6 5 4 3 2 1 0(sort)
10 10 10 10 10 5 0 0 0 0 0(cat)
10 8 6 4 2 0 0 0 0 0 0(sort-cat)
10 10 10 10 10 8 6 4 2 1 0(cat-sort)
Ambiguous vote: voters with the same interests may have different votes depending on whether they give greater importance to the category or the sorting.
Unknown favorites: in some types of vote, unknown candidates can even receive 5-8 points (type of vote 1,2,4).
The honest vote of the voter takes only one form:
34 27 20 13 6 0 0 0 0 0 0
- even in an honest vote, it makes no sense to waste limited points on unknown or negative candidates, when they could instead be given to positive candidates.
- the fact of being an honest vote avoids the accumulation of points, which will be treated in the tactical votes.
Honest votes in the DV have no ambiguity and don’t favor unknown candidates (unlike the RV).
(3) Writing a vote
Simple on paper: you only need to blacken the score box to be assigned.
Simple digital: using slider or click on the value to be assigned.
A little more complex in paper: it requires you to write the amount of points in number (which in any case doesn’t have to be 100, given that you can normalize the vote automatically before counting).
Simple digital: using sliders that automatically resize.
DV is a bit more complex to write in paper format.
(4) Counting of votes
- sum of points for each candidate.
- the candidate with the highest sum wins.
Multiple winners (most famous)
- the winning candidate is removed, and the weight of the votes is changed.
- the points are added again to find a new winner, until the desired number of winners is reached.
Ambiguity / Complexity (multiple winners): there are different formulas used to change the weight of a vote. This ambiguity makes it complex to make a voter accept why a certain formula is used rather than another.
No % of victory (multiple winners): RV returns a certain number of winners but in its standard form it doesn’t indicate how much better a candidate is than the others who have won; only the order in which they win is indicated.
Single and multiple winners
- The points are added for each candidate.
- The candidate with the smallest sum loses and is removed.
- The votes are normalized (the points assigned to the eliminated candidate are redistributed in the vote proportionally to the interests of the voter).
- Add the votes again to find a new loser to be eliminated, until reaching the desired number of winners, who are the remaining candidates.
No Ambiguity: there is only one way to normalize a score to 100 points.
Ex: [50 30 15 5 0] removing the first candidate, there would be 50 points to be redistributed proportionally, and the way to do this is only one, that is: [60 30 10 0]
Understanding (single winner): DV is a little more complex than RV because it also uses the normalization of the vote. If normalization is considered simple to understand then DV will also be simple.
Understanding (multiple winners): DV is simpler than the respective RV, because it doesn’t have the ambiguity of the RV.
% of victory: the % of victory is indicated by the sum of the points for each winning candidate left at the end.
Single winner: RV is a little easier to understand.
Multiple winners: RV has ambiguity (resulting complexity), and in the “standard form” it doesn’t return the % of victory, but only the order of victory of the candidates.
(5) Tactical Votes - Unknown Results
RV - Single winner
The tactics that a voter can use are:
- increase the points given to its positive candidates, to make them win more likely.
- decrease the points of some candidates, to decrease the probability of victory or to increase the probability of victory of others.
- increase the points given to unknown candidates, to decrease the probability of victory of negative candidates.
High influence of the tactical vote: given a set of honest voters who vote with intermediate scores: [10 9 8 7 6 5 4 3 2 1 0] a group of tactical voters (also relatively small) who vote instead only with high or low scores: [10 10 10 10 10 0 0 0 0 0 0] would be highly favored over the others.
DV - Single winner
The tactics that a voter can use are:
- accumulate points on a more preferred candidate, to favor him over the others.
In this context there are no other types of tactical voting that can be used.
Little impact of the tactical vote: eg if the honest vote of a voter is like this: [50 30 15 5 0] then his tactical vote will look like this: [90 6 3 1 0]. The example shows that if the preferred candidate is eliminated (because it is a minority), the tactical vote becomes the same as the honest one, in fact in both cases, the 100 points would be distributed proportionally as follows: [60 30 10 0].
More in general, the more points are redistributed in a tactical vote, the more the tactical vote will become equal to the honest one. During the count, tactical votes tend to become more and more similar to honest voting.
RV - Multiple winners
All the tactics listed in the single winner apply.
DV - Multiple winners
The more the number of winners increases, the more the tactical votes are reduced (they are canceled when everyone wins).
Eg honest vote: A B C D E F
This honest vote means that the voter in question wants to give: half of his power to A, one third of his power to B, one sixth of his power to C, etc. therefore for this voter the best way to represent these interests is just to vote honestly. Accumulating points on candidate A would make him go against his true interests, in this case.
RV is subject has many tactics, and the tactical vote greatly affects the result.
DV has only one tactic that during the counting (for single winner), makes the tactical vote more and more honest. Also, as the winners increase, the need to use tactical votes decreases.
All this is valid only if before voting there is no information on the possible results of the vote.
(6) Tactical Votes - Known Overall Preferences
The use of tactics in RV is expanded, based on overall preferences.
Disadvantaged minorities (single winner): if the 2 favorite candidates of the vote are known, a voter tends to assign 10 points to the preferred candidate between the two favorites and 0 points to the other, so that his vote is as influential as possible in the probable final clash between the 2 favorites.
If all the voters, who support minorities, were to reason in this way, then it would be impossible for a minority to overcome one of the two favorite candidates because both the minority and the favorite receive 10 points in the votes.
Normalization in the DV depends on how the points are distributed in the individual marks.
Knowing broadly the overall preferences of the voters doesn’t mean knowing the exact way in which a voter distributes his points in the single vote; this makes it difficult to predict how normalization will affect DV counting.
In the case of a single winner, normalization is often used so it’s difficult to create tactical votes despite knowing the overall preferences of the voters (this, compared to RV).
Doesn’t disadvantage minorities (single winner): if the 2 candidates preferred in the vote don’t like the voter, then the voter will simply have to give only 1 point out of 100 to that favorite candidate of the two, in this way:
(1) in the vote the preferred candidates (minorities) will have many more points than the candidate they don’t like (but who is favored).
(2) if the preferred candidates of the voter are actually minorities, they will all be eliminated and the 100 points will end up in the preferred candidate of the two remaining at the end, making the vote influential in the final clash (without the need to use tactical votes).
RV disadvantages minorities, unlike DV.
Normalization is difficult to exploit to create tactical votes.
(7) Monotony vs IWA
RV satisfies Monotony, but not IWA.
DV satisfies IWA, but not Monotony.
Monotony and IWA are both important but both cannot be met, so you need to understand which of the two criteria is the best to meet.
We focus on the individual winner, since it’s the context in which these criteria fail more easily.
Monotony Failure (DV)
Monotony fails when:
- by increasing the points given to a candidate, he loses
- by reducing the points given to a candidate, he wins
(1) The two tactics indicated above are likely to backfire on those who use them.
(2) If there are many people to vote, it’s also necessary that the tactics indicated above are used by a large group of specific people (not trivial).
(3) First of all, we must also make sure that we are in a vote where Monotony can actually fail. To know this, in the DV it’s necessary to know well how the voters distribute their points in the votes (since the count is based on the normalization of the votes).
Exploiting the failure of Monotony to your advantage is extremely difficult, and extremely risky.
Failure of the IWA (in RV)
- IWA fails when a new candidate is added, similar to the best (current winner) but worst of all.
Ex: R (right candidate), L (left candidate).
Those who support the right, far-right and center-right vote: R, L, and vice versa those who support the Left. In this context R wins.
Next, a far-right candidate eR is added. Far-right voters, who previously voted like this: R, L could now vote e.g. like this: eR1, R, L, removing points to R.
This behavior reduces the points of R and makes L win.
Political factions, who know the general interests of voters well, can easily create candidates to play the role of eR (spoiler), to condition the election to their advantage.
The failure of IWA can be exploited very easily when compared to the failure of Monotony, so satisfying IWA is more important.
The example also shows a huge spoiler effect problem present in the RV, but not in the DV.
(8) Downsides summary
- (2) ambiguity in honest voting (not in DV).
- (2) favors unknown candidates (not in DV).
- (4) in multiple winners it’s hard to understand and accept (because of ambiguity) and missing % victory (not in DV).
- (5) tactics: increase points to positive candidates, to increase the probability of victory.
- (5) tactics: I decrease points to the negative candidates, to decrease their probability of victory.
- (5) tactics: increase points to unknown candidates, to decrease the probability of victory of the negative candidates.
- (5) the tactical vote has a great impact on the result, in the single winner case (not in DV).
- (6) disadvantages minorities (not in DV).
- (6) easy to create tactical votes knowing the overall interests of the voters (less in DV).
- (7) the IWA fails with a consequent increase in the spoiler effect (which is worse than the failure of the Monotony).
- (3) it’s a little more complicated to write in paper form (you need to write numbers).
- (4) in the case of single winner is a bit more complicated to understand (because of normalization).
Partial defects with respect to the RV:
- (5) tactic in single winner: accumulation of points on a more preferred candidate, to favor him over the others (the tactical vote has little effect on the result, so this tactic becomes less effective).
- (7) Monotony fails (which, however, is better than the failure of the IWA).