Measuring majority power and veto power of voting rules

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of the majority’s most preferred candidates is the measure of majority power; and the minimal share of voters that allows the minority to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on such minimal shares for voting rules that are popular in the literature and used in real elections. We order the rules according to majority power and veto power. Instant-runoff voting has both the highest majority power and the highest veto power; plurality rule has the lowest. In general, the greater is the majority power of a voting rule, the greater its veto power. The three exceptions are: voting with proportional veto power, Black’s rule and Borda’s rule, which have relatively weak majority power and strong veto power, thus providing minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

     

The histoenzymological diagnosis of the time of occurrence of a closed spinal cord trauma]

Time course of the activities of transport enzymes in capillary walls of human spinal cord was studied in various periods after closed injury to the cord, inflicted by hard blunt objects, with the use of histochemical methods for the detection of alkaline phosphatase and Mg-dependent ATPase. Wave-like fluctuations in the activities of the examined enzymes were revealed. The findings may be used to assess the period elapsed since the cord injury.