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== Monotonicity ==
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The [[Monotonicity (mechanism design)#wmon|'''weak monotonicity''' property]] has a special form in single-parameter domains. A social choice function is weakly-monotonic if for every agent <math>i</math> and every <math>v_i,v_i',v_{-i}</math>, if:
: <math>Outcome(v_i, v_{-i}) \in W_i</math> and
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