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Borda Voting

Borda Voting is the simplest ordinal voting method. It is also a rating method, since each candidate gets rated with a numbered ranking.

The elector lists the options he/she likes in a specific order, and each option gets a score according to its position. Options listed first get a higher score, so you may specify that you like candidate X more than Y just by listing Y after X.

Suppose for instance there are four options n=4: then the first option in the list gets n-1 = 3 points, the second options n-2 = 2 points, the third option n-3 = 1 point and the last one gets no points at all. So, listing “B A C D” means:

B gets 3 points
A gets 2 points
C gets 1 point
D gets 0 points

Typically, in Borda method, electors are asked to list all the candidates in order to lower (but not to erase) the risk of abuses from insincere voters (see next section).

At the end, the total score for each candidate is counted and displayed as a percentage. The Borda method is theoretically very attractive, since it is relatively easy to understand and gives great expressive power to the user (effectively allowing him/her the possibility to rate the candidates in order of preference).

However, in practice, the Borda method is a rather poor method since insincere voters can easily abuse it. A simple example that shows why this is the case is reported below. If you want to use an ordinal method, which is solid against insincere votes, you should look at the Condorcet method.

Shortcomings of the Borda method

Consider an election with four candidates A, B, C and D and the sincere electoral ballot.

3: B A C D
2: A C B D

(Three votes for “B A C D” and two votes for “A C B D”). The result is:

A: 12 points
B: 11 points
C: 7 points
D: 0 points

In this case A wins over B since the last two voters, which preferred B to A, nevertheless liked A enough to put it as second choice. So, being sincere made their candidate lose the election.If B voters knew that their least preferred candidate D didn’t have any hope to win, they could have listed it over A:

1: B A C D
2: A C B D
2: B D C A

Now the result of the election would have been:

B: 11
A: 8
C: 7
D: 4

Strategically voting the weak candidate D over A made the B candidate win. Stealing points from a strong candidate and transferring them over a weak candidate is a good strategy to make middle candidates to win. So being sincere is not encouraged by the Borda method. In other words, the Borda method is not robust against insincere voters.

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Shortcomings of the Condorcet Voting method

Condorcet Voting is probably the soundest ordinal method available today and it is favoured by many academics. Nevertheless it has its own shortcomings users should be aware of.

  • The Condorcet voting method is rather complex, difficult to explain and to grasp. Also, PARTECS™ does not implement its simplest version, Plain Condorcet, but implements the SSD Condorcet method, which is even more complex to explain;
  • Condorcet results cannot easily be converted in percentages, so are difficult to read for people used to the more common voting methods;
  • Condorcet is inferior to the Borda method in the case of sincere voters, since relevant information about the relative rating is lost (but this very fact increases the robustness against insincere votes);
  • Still there are cases where Condorcet is not 100% robust against insincere voters. Below is an example of such a case.

A case where Condorcet Voting is not robust

Consider this (sincere) ballot:

40: C
35: ABC
25: BAC

Here the winner is A, who beats both B (35/25) and C (60/40). However, if the B voters strategically refuse to rank A while the A voters sincerely rank B, that will let B steal the election from A since

40: C
35: ABC
25: BC

would give the defeats:

C / A : 65/35
B / C : 60/40
A / B : 35/25

Removing the weakest defeat leaves B as the unbeaten candidate. Instant runoff and Borda method do not have this problem: voting C insincerely will go against the interest of B voters, since C will win, not B. However, it may be argued that these methods have even worse problems than Condorcet.

What about ties?

In elections with a small number of voters (typical of decision making process in small committees), ties are relatively frequent and must be managed in some way. There are various ways to solve the ambiguities, for instance the President may decide, or a different voting method can be used to see if the ambiguity disappears. Here is an example with four candidates A, B, C, D and these votes by a six members committee:

3: A C
3: B A

Nobody likes D, whereas three voters like A and three voters like B, but B voters also like A as a second choice, so we would expect A to win. However this is not the case using the Condorcet method, nor the Instant Runoff method. Let us consider first the Condorcet method tallying procedure. The defeats are:

A / D : 6/0
A / C : 6/0
C / D : 3/0
B / D : 3/0

Dropping the weakest defeats we still have a tie between A and B since they are both unbeaten. Still, it is clear that A must be winner, since it gets both first and second choices. The ambiguity is removed by the Borda method:

A: 15
B: 9
C: 6
D: 0

Condorcet Voting tends to give more ties than other methods. This is a good thing in general, since it is better to return a tie in dubious cases, leaving the decision to a human, than to return a wrong result. Now, let’s check if the Instant Runoff method gives a tie too:

This election required 2 rounds.
Round #1:
Removing D ...
3: A C -
3: B A -
Round #2:
Removing C ...
.TIE EXCEPTION: 

No winner can be established, since the algorithm cannot decide the weakest candidate between A and B.

Il Memorandum del Dipartimento di Difesa USA sul Software Libero/Open Source

Non so se avete già letto il memorandum del dipartimento di difesa degli stati uniti per il software libero/open source

Mentre secondo me inizia bene…

“2. GUIDANCE
a. In almost all cases, OSS meets the definition of “commercial computer software” and shall be given appropriate statutory preference in accordance with 10 USC 2377 (reference (b)) (see also FAR 2.101(b), 12.000, 12.101 (reference (c)); and DFARS 212.212, and 252.227-7014(a)(1) (reference (d))).”

e poi continua con una ragionevole spiegazione sui tipi di licenze aperte….

“e. There is a misconception that the Government is always obligated to distribute the source code of any modified OSS to the public, and therefore that OSS should not be integrated or modified for use in classified or other sensitive DoD systems. In contrast, many open source licenses permit the user to modify OSS for internal use without being obligated to distribute source code to the public. However, if the user chooses to distribute the modified OSS outside the user’s organization (e.g., a Government user distributes the code outside the Government), then some OSS licenses (such as the GNU General Public License) do require distribution of the corresponding source code to the recipient of the software. For this reason, it is important to understand both the specifics of the open source license in question and how the Department intends to use and redistribute any DoD-modified OSS.”

mi pare di capire che non finisca proprio bene, in particolare per una frase (evidenziata qui sotto in grassetto) che o è stata scritta male (dovrebbe essere “or when pre-existing OSS for which the Government is the copyright holder is modified…”) oppure è stata messa li apposta per “chiarire” (?) che il Governo USA è sopra ogni licenza (ed ogni libertà)…

“g. Software […] developed for the Government should be released to the public (such as under an open source license) when all of the following conditions are met:
[…]
(2) The Government has the rights to reproduce and release the item, and to authorize others to do so. For example, the Government has public release rights when the software is developed by Government personnel, when the Government receives “unlimited rights” in software developed by a contractor at Government expense, or when pre-existing OSS is modified by or for the Government.
[…]”

Voi che impressione avete ?

Vazou! A Rede Social do PSL-Brasil

A menos de 24 horas do lançamento oficial da plataforma, vazou pelo twitter a URL de teste! Veja o tweet que escapou das maos de um de nossos beta-testers que, desavisado, “quebrou o protocolo” e vazou o link…

vazou_rede_pslbrasil.png

O tweet original foi apagado… A URL continua no ar… mas talvez nao por muito tempo…

Ai vai um screenshot:

software-livre-brasil_1243611183438.png