Computational application of the mathematical theory of democracy to Arrow’s Impossibility Theorem (how dictatorial are Arrow’s dictators?)

The article is based on three findings. The first one is the interrelation between Arrow’s (Social choice and individual values, Wiley, New York, 1951) social choice model and the mathematical theory of democracy discussed by Tangian (Aggregation and representation of preferences, Springer, Berlin, 1991; Soc Choice Welf 11(1):1–82, 1994), with the conclusion that Arrow’s dictators are less harmful than commonly supposed. The second finding is Quesada’s (Public Choice 130:395–400, 2007) estimate of their power as that of two voters, implying that Arrow’s dictators are not more powerful than a chairperson with an additional vote. The third is the model of Athenian democracy (Tangian, Soc Choice Welf 31:537–572, 2008), where indicators of popularity and universality are applied to representatives and representative bodies. In this article, these indicators are used to computationally evaluate the representativeness/non-representativeness of Arrow’s dictators. In particular, it is shown that there always exist Arrow’s dictators who on the average share opinions of a majority, being rather representatives. The same holds for dictators selected by lot, which conforms to the practice of selecting magistrates and presidents by lot in ancient democracies and medieval Italian republics. Computational formulas are derived for finding the optimal “dictator–representatives”.     

Robot Map Verification of a Graph World

In the map verification problem, a robot is given a (possibly incorrect) map M of the world G with its position and orientation indicated on the map. The task is to find out whether this map, for the given robot position and its orientation in the map, is correct for the world G. We consider the world model of a graph G = (V _G, E _G) in which, for each vertex, edges incident to the vertex are ordered cyclically around that vertex. (This also holds for the map M = (V _M, E _M.) The robot can traverse edges and enumerate edges incident on the current vertex, but it cannot distinguish vertices (and edges) from each other. To solve the verification problem, the robot uses a portable edge marker, that it can put down at an edge of the graph world G and pick up later as needed. The robot can recognize the edge marker when it encounters it in the world G. By reducing the verification problem to an exploration problem, verification can be completed in O(|V _G| × |E _G|) edge traversals (the mechanical cost) with the help of a single vertex marker which can be dropped and picked up at vertices of the graph world (G. Dudek, M. Jenkin, E. Milios, and D. Wilkes, IEEE Trans. on Robotics and Automation, vol. 7, pp. 859–865, 1991; Robotics and Autonomous Systems, vol. 22(2), pp. 159–178, 1997). In this paper, we show a strategy that verifies a map in O(|V _M|) edge traversals only, using a single edge marker, when M is a plane embedded graph, even though G may not be planar (e.g., G may contain overpasses, tunnels, etc.).     

Employer brand building for start-ups: which job attributes do employees value most?

Although attracting talented personnel is one of the biggest challenges for start-ups, little is known about how nascent ventures can successfully build an employer brand. This study investigates which distinctive job attributes start-ups can use for their employer branding. We identify the unique job attributes distinguishing entrepreneurial firms from large firms and calibrate the relative value of these job attributes from the potential employees’ perspective. Using conjoint analysis we demonstrate that a communal team climate and the early assignment of responsibilities are a start-up’s most attractive job attributes for prospective applicants. We contribute to the entrepreneurial marketing literature by bringing forward the concept of entrepreneurial employer branding, by examining entrepreneurial firms’ unique and attractive job attributes, and by discussing how start-ups can make use of these attributes in their recruiting and employer branding activities.     

Employer Branding: A Brand Equity‐based Literature Review and Research Agenda

Over the past two decades, scholarly interest in employer branding has strongly increased. Simultaneously, however, employer branding research has developed into a fragmented field with heterogeneous interpretations of the employer branding concept and its scope, which has impeded further theoretical and empirical advancement. To strengthen the foundation for future work, this paper takes a brand equity perspective to review the extant literature and create an integrative model of employer branding. Using an analytical approach, the authors identify 187 articles, which they integrate along different employer brand dimensions and branding strategies: (i) conceptual; (ii) employer knowledge dimensions; (iii) employer branding activities and strategies. On the basis of this review, the authors develop an employer branding value chain model and derive future research avenues as well as practical implications.     

German parliamentary elections 2009 from the viewpoint of direct democracy

The mathematical theory of democracy is applied to analyze the German Bundestag elections 2009 and to evaluate five German leading parties and their coalitions from the viewpoint of direct democracy. For this purpose, the positions of the parties on over 30 topical issues are compared with results of public opinion polls. The outcomes are summarized in the party indices of popularity (the average percentage of the population represented) and universality (frequency of representing a majority). It is shown that the election winner 2009, the conservative party CDU/CSU, has a quite low representativeness (ranked fourth), whereas the most representative is the left party die Linke which received only 11.9% votes. It is concluded that voters are not very consistent with their own political profiles, disregard party manifestos, and are likely driven by political traditions, even if outdated, or by personal images of politicians. To bridge approaches of representative and direct democracy, some modifications to the election procedure are proposed, which, among other things, complicate vote manipulations.     

A mathematical model of Athenian democracy

It is shown that the representative capacity of democratic institutions selected by lot (=lottery), as it has been practiced in Athens in 594–322BC, is quite high. For this purpose, People’s Assembly, Council of 500, Committee of 50 with its President, juries, and magistrates are evaluated with indicators of popularity, universality, and goodness. The popularity is a spatial characteristic of representativeness, the average percentage of the population whose opinion is represented on a number of questions. The universality is a temporal aspect of representativeness, the frequency of cases (percentage of questions) when the opinion of a majority is represented. The goodness is the specific representativeness, that is, the average group-represented- to-majority ratio. In particular, it is shown that the size of Athenian representative bodies selected by lot was adequate to guarantee their high representativeness. The background idea is the same as in Gallup polls of public opinion and in quality control based on limited random samples.