Monotone Voting Rule (COMSOC)

Definition

Monotone Voting Rule ( COMSOC)

A voting rule is monotone if raising a winning alternative in one voter’s ranking cannot make it lose. For profiles $R,R^{\prime }$ over the same voters and alternatives,

$$\begin{array}{l}x\in \lambda (R),\\ R^{\prime }\text{ is obtained by raising }x\text{ in one ballot}\end{array}\}⟹x\in \lambda (R^{\prime }).$$

Raising $x$ preserves the relative order of every other alternative; all other ballots stay unchanged. Repeating this operation allows several voters to raise $x$. The requirement preserves winner status, not necessarily the entire winner set.

Only the changed ballot is shown: $A$ passes $C$, while $B\succ C\succ D$ stays unchanged. The diagram states the required behaviour, not the outcome of a particular rule.