Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective Bias Models in Two-Tier Voting Systems and the Democracy
  Deficit   We analyse optimal voting weights in two-tier voting systems. In our model,
the overall population (or union) is split in groups (or member states) of
different sizes. The individuals comprising the overall population constitute
the first tier, and the council is the second tier. Each group has a
representative in the council that casts votes on their behalf. By `optimal
weights', we mean voting weights in the council which minimise the democracy
deficit, i.e. the expected deviation of the council vote from a (hypothetical)
popular vote.
  We assume that the voters within each group interact via what we call a local
collective bias or common belief (through tradition, common values, strong
religious beliefs, etc.). We allow in addition an interaction across group
borders via a global bias. Thus, the voting behaviour of each voter depends on
the behaviour of all other voters. This correlation is stronger between voters
in the same group, but in general not zero for voters in different groups.
  We call the respective voting measure a Collective Bias Model (CBM). The
`simple CBM' introduced by Kirsch (2007) and in particular the Impartial
Culture and the Impartial Anonymous Culture are special cases of our general
model.
  We compute the optimal weights for large groups rather explicitly. Those
optimal weights are unique as long as there is no `complete' correlation
between the groups. If the correlation between voters in different groups is
extremely strong, then the optimal weights are not unique at all. In fact, in
this case, the weights are essentially arbitrary.

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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg