
doi: 10.5772/12917
The relevance of the Traveling Salesman Problem (TSP), or the Traveling Salesperson Problem, is large and an indication of that it is the fact the present book is not the first(Applegate et al., 2006; Lawler et al., 1985; Gutin & Punnen, 2007). In this chapter we do not define the problem, neither offer new and faster way of solution, we present, instead, an application of TSP to sociophysics. The specific problem we deal here is to offer a dynamical explanation to the vote distribution of some corporations, i.e. the corporate vote. Recently, this distribution was described for the ruling party inMexico during the majority of the XX century. With the arrival of the new millennium such a party became opposition, but it keep part of the organization which gave it a large power during seven decades. In reference (Hernandez-Saldana, 2009) the distribution of votes of this political party during the newmillennium elections was described very well by the so called daisy models of rank r (Hernandez-Saldana et al., 1998). However, the physical origins of these models makes hard to establish a direct link with a socio-political phenomena. In order to explore a solution to this problem a TSP approach was proposed in (Hernandez-Saldana, 2009) and analyzed in (Hernandez-Saldana et al., 2010). In the present chapter we offer an integrated and detailed exposition of the subject. In recent years the analysis of the distribution of votes from the point of view of statistical physics has been of interest. The analysis include the proportional vote in Brazil (Filho et al., 1999; 2003; Bernardes et al., 2002; Lyra et al., 2003); India and Brazil (Araripe et al., 2006); India and Canada (Sinha & Pan, 2006); Mexico (Morales-Matamoros et al., 2006) and Indonesia (Situngkir, 2004). A statistical analysis of election in Mexico (Baez et al., 2010) and Russia (Sadovsky & Gliskov, 2007) has been realized. Several models appeared in order to understand why we vote as we do (Fortunato & Castellano, 2007) or a study of the spatial correlations of the voting patterns (Borghesi & Bouchaud, 2010). The analysis of this problem is only one aspect of two new branches in physical sciences: the sociophysics and the econophysics. For an illuminating exposition of the former topic see the book of P. Ball (Ball, 2004), and for the latter consult the book of R.N. Mantegna (Mantegna & Stanley, 2000). But, how to use TSP to model votes?. The idea is compare the statistical properties of the number of votes obtained for a political party in each cabin with the distance between cities in a TSP. The way to compare pears(votes) with apples(distances) is to map them to new variables where their statistical properties could be compared. Such a process is named, for historical reason, unfolding and we shall devote subsection 3.1 to explain carefully how this is performed. The idea is to measure in a dimensionless variable with density one. This approach has been successful analyzing fluctuation properties in a large set of problems, 16
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