Monotonicity Cut Off Points

CHAPTER 1: THE SIMPLE LOGIC OF STORABLE VOTES
According to Casella (2012:4), members or voters have preferences over whether any specific proposal should pass or fail.
Every person or voter knows his own preferences over all proposals but does not know preferences of other voters. Proposals are unrelated and preferences are independent across proposals and individuals.
Before agenda and proposals are specified, no member expects to be systematically biased toward a favourable or negative position. Once proposals are known, members are unable to predict each other’s preferences. Everybody knows the probability distribution from which preferences are drawn (Casella, 2012:5).
Proposals are voted upon sequentially and each voter has one regular

when the intensity of preferences become strong enough to do so. The decision on which cut-off point to choose is totally arbitrary in nature.
The decision of wrong intensity cut-points does not have a large effect on proving monotonicity in voting strategies, as errors (deviations from perfect monotonicity) are small and can be trivial. This however is not the case in analyzing equilibrium strategies, and the choice of cut-off points become more important.
Experimental data supports monotonicity in voting strategies but not equilibrium behavior..
Casella (2012) shows that experimental data almost perfectly matches the predictions from theory of storable votes for all group sizes and number of proposals.
The experimental data also indicates that storable votes lead to larger surplus gains relative to predictions from a majority voting mechanism, although the data is much more dispersed and even indicate that under some circumstances majority voting might lead to higher welfare

The referendums are not related.
Golden Voting Rule – voters cannot gain by voting against their preferences thus voters will vote sincerely. when choosing the referendum over which to cast the bonus vote, an individual considers two things, namely: how much value he puts on the various referendums, all else equal, the individual must cast the bonus vote on the referendum that they value the most, “one that is their highest priority and also consider the impact of the bonus vote on the pivot probability, the probability that one’s own vote will change the outcome.
Lastly, Casella (2012:142) cautions, if storable votes are to be used in referendums, it is important to check how the voting mechanism will behave when certain aspects of its assumptions are weakened.
For instance, the assumption that preferences are identically distributed over all proposals is, unrealistic in the context of referendums. Many issues put to referendums are typically of interest only to a small minority – same sex marriage, the draft of a constitution for the European Union and