Consider the following voting game:
There are three candidates, each of whom chooses a position from the set $S_i = \lbrace 1, 2,...,10 \rbrace$. The voters are equally distributed across these ten positions. This means at each position, there are 10% of the available votes. Voters vote for the candidate whose position is closest to theirs. If the three candidates are equidistant from a given position, the voters at that position split their votes equally. Thus, for example, $u_1(8, 8,8) = 33.3$ ( this means the candidate $1$ choosing position $8$ with other two candidates also choosing position $8$ will get about 33.3% of the total available votes, and similarly $u_1(7,9,9) = 73.3$.
Now the problem is
Is strategy $1$ dominated, strictly or weakly, by strategy $2$? How about by strategy $3$? By "strategy $1$", I mean the strategy of choosing position $1$. Similarly for others.