We provide elementary proofs of results from \mbox{%DIFAUXCMD Saari0pt%DIFAUXCMD and \mbox{%DIFAUXCMD DEMO }0pt%DIFAUXCMD regarding }  the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile. The analysis ultimately boils down to considering the image of the fundamental chamber of the essentialization of the braid arrangement under linear maps described by doubly stochastic matrices.
We provide elementary proofs of 0pt%DIFAUXCMD and \mbox{%DIFAUXCMD DEMO }0pt%DIFAUXCMD regarding } several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile. The analysis ultimately boils down to thinking about positional voting systems in terms of doubly stochastic matrices.
D
results from \mbox{%DIFAUXCMD Saari
A
several results concerning
R
considering the image of the fundamental chamber of the essentialization of the braid arrangement under linear maps described by
thinking about positional voting systems in terms of