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Provided are a natural extension of the Borda count to the n-dimensional spatial context, & an algorithm to find the spatial Borda winner based on the notion of an inverse Borda count. The result is that the Borda winner & the Condorcet winner coincide in unidimensional space when all alternatives on a line are feasible. Results show that in multidimensional space, the Borda winner & the Condorcet winner will be distinct. Results are also provided on the manipulability of outcomes under the Borda rule as a function of the domain of alternatives over which the Borda count is to be defined. 2 Figures, 21 References. HA

In this paper, we consider a fuzzy variant of the Borda count taking into account agents' intensities of preference. This fuzzy Borda count is obtained by means of score gradation & normalization processes from its original pattern. The advantages of the Borda count hold, & are even improved, providing an appropriate scheme in collective decision making. In addition, both classic & fuzzy Borda counts are related to approval voting, establishing a unified framework from distinct points of view. 2 Tables, 55 References. Adapted from the source document.

The election of 1860 was one of the most important and contentious elections in US history. It was also one of the most interesting. Four candidates from three different parties battled for the presidency and all four received a significant number of votes. We ask whether Lincoln's victory was sound, or was it due to a fluke in the electoral system? Did a Lincoln win plausibly represent the will of the voters or would a different voting system have represented their preferences more accurately? Would the outcome have been the same had one or more of the candidates dropped out of the race? These and other questions are answered using new graphical techniques which let us assess voter preferences more accurately. Using these techniques, we are able to show, in a single figure, the outcome of every positional voting system, as well as all possible approval voting outcomes. By comparing the outcome under plurality rule to the outcomes which would have occurred under other voting systems, we conclude that Stephen Douglas, not Lincoln, was plausibly the candidate who best represented the preferences of the voters.