Distributed Voting: Difference between revisions

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Reversed vote, made negative: A[0] B[-2] C[-4] D[-6] E[-8] F[-9]
Reversed vote, made negative: A[0] B[-2] C[-4] D[-6] E[-8] F[-9]


''Reversing and making negative means that the voter's 100 points are used to disadvantage the worst from winning. This procedure reduces the failure of monotony, for the single-winner case.''
''Reversing and making negative means that the voter's 100 points are used to disadvantage the worst from winning (points will be always negative in the counting). This procedure reduces the failure of monotony, for the single-winner case, and increases resistance to min-maxing strategies.''


==Ballot==
==Ballot==
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P = 100 (can also be set to 1).
P = 100 (can also be set to 1).
S = points sum of the candidates remaining in the vote, after an elimination.
S = points sum of the candidates remaining in the vote, after an elimination.
V = old value of candidate X.
V = old points value of candidate X.
newV = new value of candidate X.
newV = new points value of candidate X.
<math>\begin{equation}
<math>\begin{equation}
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===[[IRNR]]===
===[[IRNR]]===


[[IRNR]] (L1 norm) is applied on rating ballots, also on ranges with negative values such as [-5,+5]. Distributed Voting (not extended), in the [[Single Member system|Single-Winner]] context, is a subcategory of IRNR, which binds the minimum value of the rating ballots to 0 (doesn't accept ratings with negative values). This constraint is important because it avoids the ambiguity of the IRNR:
[[IRNR]] (L1 norm) is applied also on ranges with negative values such as [-5,+5] but this makes it subject to ambiguity.


Range [0,10] with IRNR and Distributed Voting
Range [0,10] with IRNR
61: A[10] B[6] C[0]
61: A[10] B[6] C[0]
39: A[0] B[6] C[10]
39: A[0] B[6] C[10]
Eliminated in order C,A.
Eliminated in order C,A.
B wins.
B wins.
IRNR and Distributed Voting are equivalent in this case.


Range [-5,+5] with IRNR
Range [-5,+5] with IRNR
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A wins.
A wins.


In IRNR only by changing the extremes of the range (leaving the interests of the voters and the size of the range unchanged), the winner changes. Distributed Voting instead avoid this ambiguity by imposing 0 as the minimum value in the rating.
In IRNR only by moving the range in negative value (leaving the interests of the voters and the size of the range unchanged), the winner changes. Distributed Voting instead avoid this ambiguity by imposing 0 as the minimum value in the range.

IRNR is a [[Single Member system|Single-Winner system]] which also, unlike Distributed Voting, doesn't reverse and make negative the vote before the count.



==Related Systems ==
==Related Systems ==
⚫
* [[Instant Runoff Normalized Ratings]] (ratings also negative, and it doesn't reverse and make negative the vote)
* [[Distributed Multi-Voting]] (particular vote conversion)
⚫
* [[Instant Runoff Normalized Ratings]] (ratings also negative)
* [[Baldwin's method]] (Borda, and variant with different normalization)
* [[Baldwin's method]] (Borda, and variant with different normalization)


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