The island of Frobnitz is trying to decide whether to legalize left-handed quonkbats. Three million voters are represented by 200 members of parliament. In a referendum, a majority voice support for the measure, so it goes before parliament … which rejects it.
Why? Because most of the MPs’ constituencies oppose it:
With this distribution, more than 55 percent (1,664,000/3,000,000) of the referendum votes are positive, but still more than 5/6 (167/200) of the MPs must vote no if they are to honor the preferences of their supporters.
In Voting Paradoxes and How to Deal With Them (1999), Hannu Nurmi writes, “The practical significance of the referendum paradox is in the shadow it casts on the institution of consultative referendum. Which should be decisive: the majority of the votes cast in a referendum or the majority of the votes of representatives who believe to represent the views of the majority of their supporters? If the former is considered more decisive, why then resort to the latter at all? If the latter is regarded as more important, then why bother with the former at all?”