After introducing a way to analyze positional voting outcomes in a spatial voting context, ‘core’ type theorems are proved for these voting rules, and their runoffs, in the single issue setting. While spatial voting has proved to be a valuable way to interject geometry and geometric intuition into the analysis of voting rules, the current methodology is essentially limited to pairwise compariso...

Remote Internet voting places the control and secrecy of the immediate voting environment on the shoulder of the individual voter but it also turns voting into yet another on-line activity thus endangering the well-known social nature of voting and possibly reducing the crucial sense of civic duty that is important for a healthy democracy. There is however a complete lack of evidence to what de...

We compare voluntary and compulsory voting in a Condorcet-type model in which voters have identical preferences but differential information. With voluntary voting, all equilibria involve sincere voting and positive participation. Thus, in contrast to situations with compulsory voting, there is no conflict between strategic and sincere behavior. When voting is costless, voluntary voting is welf...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...