## DIMACS TR: 2004-06

## War and Peace in Veto Voting

### Author: Vladimir Gurvich

**
ABSTRACT
**

Let $I = \{i_1, \ldots, i_n\}$
be a set of voters (players) and
$A = \{a_1, \ldots, a_p\}$
be a set of candidates (outcomes).
Each voter $i \in I$ has a preference $P_i$
over the candidates.
We assume that $P_i$ is a complete order on $A$.
The preference profile $P = \{P_i, i \in I\}$
is called a {\em situation}.
A situation is called {\em war} if
the set of all voters
$I$ is partitioned in two coalitions $K_1$ and $K_2$
such that all voters of $K_i$ have the same preference,
$i = 1,2,$
and these two preferences are opposite.
For a simple class of veto voting schemes
we prove that
the results of elections in all war situations
uniquely define the results
for all other ({\em peace}) situations.
Key words:
veto, voting scheme, voting by veto,
veto power, veto resistance,
voter, candidate, player, outcome, coalition, block,
effectivity function, veto function,
social choice function, social choice correspondence

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2004/2004-06.ps.gz

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