Voting by Committees under Constraints



Moreover, this section is minimal since neither {ж} nor {y} are sections
because, for instance,
AC ({ж}) = {0, {ж}} but

Φ (в) = {ц + {в, ω} + {в, {2} .m) + {{>■}. o∙. «}} + {», w}
and

({≈}) = {6} + {0,{z} . {z,w}} + {{r} . {i>,<∕}} + {0. {«}} ,

and hence, C'j'' (0) ≠ C, ,∙!ι'})

Also, {^,w} is a section because AC ({z, w}) = {0, {z} , {z, w}} (notice
that the subset {w} is not an active component of
{z, w}) and CfCw's (0),
^,w} and
ρAA       are an equal to

W + {0,W,M} + {W,⅛Q}} + {0,{t}}∙

Moreover, this section is minimal since neither {z} nor {w} are sections
because, for instance,
AC ({w}) = {0, { w } } but

4"1 (0) = {!>} + {0. Ы . {y}} + {0. {z}} + {{r} . {i>,<∕}} + {0. {«}}
and

4”’ (W) = {4 + {0. w. ⅛}} + w + {{и, {∙s,9}} + {0, и,

and hence, C^ (0) ≠ C^ ({w}).

The proof that all other components of the decomposition are also mini-
mal sections is similar and left to the reader.

Now, given a set of agents N, any voting by committees /■': A" → 2λ
will be strategy-proof as long as it satisfies the following properties: (a) by
condition (3) of Theorem 1, W''' = W(" = {¼}} and TV™ = W™ = {{⅛}}
for some
ii,i2 N; (b) by condition (1) of Theorem 1, W('' = TV™; and (c)
by condition (2) of Theorem 1, TVr and TVs are complementary.

17



More intriguing information

1. GOVERNANÇA E MECANISMOS DE CONTROLE SOCIAL EM REDES ORGANIZACIONAIS
2. The name is absent
3. Foreign Direct Investment and Unequal Regional Economic Growth in China
4. Dual Inflation Under the Currency Board: The Challenges of Bulgarian EU Accession
5. The name is absent
6. Short report "About a rare cause of primary hyperparathyroidism"
7. The name is absent
8. Regional dynamics in mountain areas and the need for integrated policies
9. Social Irresponsibility in Management
10. Does Market Concentration Promote or Reduce New Product Introductions? Evidence from US Food Industry