1.15. Consider the Supreme Court as an electorate of 9 members that votes yes-or-no on a variety of issues. It is customary for this electorate to use the simple majority method, and since 9 is an odd number, no ties can result when no justices are absent. Imagine the following alternative method for determining Supreme Court decisions. The decision is affirmative whenever at least 3 of the first 5 justices vote to affirm. Otherwise the decision is negative. This is just the bloc voting method, where the justices form blocs of size 5, 1, 1, 1, and 1. (This method emulates what would occur if the first 5 justices were to agree to always vote as a bloc and to decide among themselves how the bloc should rule.) (a) Is this method anonymous? (b) Is this method neutral? (c) Is this method monotone?
urgent
1.15. Consider the Supreme Court as an electorate of 9 members that
votes yes-or-no on a variety of issues. It is customary for this electorate
to use the simple majority method, and since 9 is an odd number, no ties
can result when no justices are absent. Imagine the following alternative
method for determining Supreme Court decisions. The decision is affirmative whenever at least 3 of the first 5 justices vote to affirm. Otherwise
the decision is negative. This is just the bloc voting method, where the
justices form blocs of size 5, 1, 1, 1, and 1. (This method emulates what
would occur if the first 5 justices were to agree to always vote as a bloc
and to decide among themselves how the bloc should rule.)
(a) Is this method anonymous?
(b) Is this method neutral?
(c) Is this method monotone?
(d) If you were one of the 4 justices not among the first 5, why would
you complain about this voting method?
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