DeepAI

# Parameterized Intractability for Multi-Winner Election under the Chamberlin-Courant Rule and the Monroe Rule

Answering an open question by Betzler et al. [Betzler et al., JAIR'13], we resolve the parameterized complexity of the multi-winner determination problem under two famous representation voting rules: the Chamberlin-Courant (in short CC) rule [Chamberlin and Courant, APSR'83] and the Monroe rule [Monroe, APSR'95]. We show that under both rules, the problem is W[1]-hard with respect to the sum β of misrepresentations, thereby precluding the existence of any f(β) · |I|^O(1) -time algorithm, where |I| denotes the size of the input instance.

• 25 publications
• 7 publications
12/05/2018

### Voting and Bribing in Single-Exponential Time

We introduce a general problem about bribery in voting systems. In the R...
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### More Effort Towards Multiagent Knapsack

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We introduce simple quadrature rules for the family of nonparametric non...
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### Robustness of Greedy Approval Rules

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### Gerrymandering Trees: Parameterized Hardness

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### Near-Tight Algorithms for the Chamberlin-Courant and Thiele Voting Rules

We present an almost optimal algorithm for the classic Chamberlin-Couran...
10/15/2022

### Beyond the Worst Case: Semi-Random Complexity Analysis of Winner Determination

The computational complexity of winner determination is a classical and ...