Reciprocal Score Voting: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 7:
Let <math>B^{v|\phi}_j</math> be the ballot rating of the <math>v</math>-th voter towards candidate <math>j</math>, where <math>\phi</math> is the set of factions assigned to that voter. This means <math>B^{v|\phi}_j > B^{v|\phi}_k</math> for all <math>j \in \phi, k \notin \phi</math>. Define <math>F_{i \to j}</math> be the mean rating given by faction <math>i</math> to faction <math>j</math>, and also that <math>F_{i \to \phi} = \frac{1}{|\phi|} \sum_{j \in \phi} F_{i \to j}</math>, that is, the mean of the rating given to all members of that set of factions, and similarly for <math>F_{\phi \to j}</math>.
:<math>B^{v|\phi}_j \mapsto B^{v|\phi}_j \min\left( \frac{ F_{j \to \phi} }{ F_{\phi \to j} } , 1 \right)</math>,
that is, factions only
Only when factions agree on their mutual ratings and perfectly reciprocate is that their ''reciprocity ratio'' <math>\frac{ F_{j \to \phi} }{ F_{\phi \to j} } = 1</math>, in which case votes are left unchanged.
In the case of any asymmetry in support, the reciprocity ratio is <math>\frac{ F_{j \to \phi} }{ F_{\phi \to j} } < 0</math> for the faction which did not cooperate, and <math>\frac{ F_{j \to \phi} }{ F_{\phi \to j} } = 1</math> for the faction that
Therefore, not cooperating penalizes the side which did not cooperate more. In this way, factions are encouraged to cooperate as much as possible to maximize mutual support, forcing them to strike a balance between supporting their favorite as well as supporting alternatives as much as they can.
This system suffers from a very unusual "reverse spoiler effect", in which a larger faction may lose an election by not supporting smaller supportive factions. In this way, larger factions are encouraged to promote smaller factions as much as possible.▼
▲This system is non-monotonic and suffers from a very unusual "reverse spoiler effect", in which a larger faction may lose an election by not supporting smaller supportive factions.
The <math>\min(\cdot, 1)</math> condition above is required so that support is never amplified by asymmetry. This is also necessary so that a smaller faction cannot parasite on the support of a larger faction, which will never rate the smaller faction above its own. A smaller faction artificially rating a larger faction too highly will only receive exactly as much support as the larger faction is willing to give it.
| |||