The difference between a proportional system and a winner-takes-all system is in the amount of representation the minority gets following a vote.
In a winner-takes-all system, the losing party, regardless of how many votes they received, does not receive any share in representation. For example, one party may receive 51%...
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of the vote while the other receives 49% of the vote. Despite the fact that a significant amount of the vote went to the losing party, they would receive no representation because they did not win. This can lead to division, anger, and frustration from the minority party.
In a proportional representation system, the party receiving 49% of the vote should receive close to 49% of the representatives. Many see this as a more fair system, because it does not leave the minority party's voters without any representation.
The difference between these two is that, in a winner take all system, a party that does not win the plurality of the votes does not get any representation. In a proportional representation system, a party can get representation even if it does not win the election.
Let us imagine that three parties run in an election. One gets 50%, one gets 30%, and one gets 20% of the vote. In a WTA system, only the first party gets represented. This is not proportional. In a PR system, the parties would get representatives in proportion to the votes they got. If there were 10 representatives, the first party would get 5, the second party 3, and the third party 2. This is why many people feel this sort of system is fairer than a WTA system.