For example, suppose our voting blocs have the following preferences regarding independent decisions X and Y. (Capitalization indicates the presence or absence of a provision, so "XY" means the bill contains both provisions X and Y, whereas "Xy" means X is present but Y is absent.)
Bloc size | Preference |
---|---|
35% | Xy > XY > xy > xY |
33% | xY > XY > xy > Xy |
32% | xy > others |
Note that a large 68% majority would prefer the bill XY to pass vs. the status quo of neither X nor Y. However, if these provisions are voted on independently, X fails by a 65% to 35% majority vote. And Y fails by a 67% to 33% majority vote. (The effect is more dramatic if we use utilities instead of mere ordinal preferences.)
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