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Medientyp:
E-Artikel
Titel:
Consensus Signed Digraphs
Beteiligte:
Weeks, Jeffrey R.;
Bogart, Kenneth P.
Erschienen:
Society for Industrial and Applied Mathematics, 1979
Erschienen in:SIAM Journal on Applied Mathematics
Sprache:
Englisch
ISSN:
0036-1399
Entstehung:
Anmerkungen:
Beschreibung:
<p>In his work on signed diagraphs and energy demand problems, F. S. Roberts mentions the need for a good method of obtaining a consensus signed digraph of a collection of signed digraphs. On the basis of work by Kemeny and Snell, and Bogart, we axiomatically define two distance functions on the space of all signed digraphs and the space of all weighted digraphs on a given vertex set. Following Kemeny's definitions of means and medians of subsets of metric spaces, we analyze the median of a collection of signed (weighted) digraphs relative to one of these distances and the mean relative to the other. (Mathematical considerations led us to analyze the median for one and the mean for the other.) Simple algorithms are given for finding the mean and median of a collection. We analyze a consensus method proposed by Roberts, and specify when the consensus will be a good one according to our criteria. Finally, we propose a new consensus method which, in our opinion, is good in all cases.</p>