Is the multi-party system a threat to democracy?

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On the contrary, multi-party systems are if anything more democratic.

Given the large number of people in a nation-state and the wide array of political issues people care about, from tax rates to women's rights to declarations of war, it would be wildly improbable for everyone's political views to be consistently aligned with one of only two parties. By having many parties, a democratic state can more accurately reflect the will of its diverse population.

For example, suppose there are three types of voters, A, B, and C, each comprising a third of the population, and they care about two issues: What flavor of ice cream to buy, and how wide the roads should be. (I'm choosing silly issues intentionally to avoid any preconceptions.)

A voters want chocolate ice cream and wide roads.

B voters want vanilla ice cream and wide roads.

C voters want vanilla ice cream and narrow roads.

Suppose everyone's preference for ice cream flavor is stronger than their preference for road width. Notice that most people want wide roads, and most people want vanilla ice cream.

Now suppose there are only two parties: Chocolatists support chocolate ice cream and wide roads, while Vanillists support vanilla ice cream and narrow roads.

Because everyone prioritizes ice cream flavor, A voters vote Chocolatist. B voters vote Vanillist. C voters will also vote Vanillist. Vanillists will win and we'll have vanilla ice cream and narrow roads, even though most people wanted wide roads.

But now if a third party came into play, the Wideroadists who support wide roads and vanilla ice cream, now A voters would still vote Chocolatist, but B voters would vote Wideroadist, and C voters would still vote Vanillist. If this is a legislature with voting coalitions, then we'd have wide roads (a Wideroadist-Chocolatist coalition) and vanilla ice cream (a Vanillist-Wideroadist coalition); this would best reflect popular will.

There are a few advantages to two-party systems: they are simple for voters to understand, and if public opinion is largely polarized they can protect the majority against the minority in certain cases. It's rare for extreme views to become represented in two-party states, but it's about as rare for extreme views to actually result in legislation in multi-party states.

In general these are outweighed by the advantages of multi-party states: Better expression of the public will, more opportunities for compromise, fewer opportunities to game the system with strategic voting or campaigning, and typically greater engagement and turnout among voters, who feel their opinions are really being represented.

As a result, a two-party system is really not so much a desirable system to try to achieve, as it is the all-but-inevitable outcome of a winner-takes-all plurality vote. There's also not much incentive for politicians who win in a two-party system to try to change to a multi-party system, whereas there can be incentives for politicians who win some seats in a multi-party system to try to make a two-party system to win even more seats.

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