Different types of voting can lead to different results

Source - Economist, July 21, 2018: "Here we go again?"     

Different types of voting can result in different outcomes. A new Brexit referendum seems likely but the type of voting method chosen could dictate the outcome. 

Types of Voting

By law, Theresa May cannot sign a Brexit deal without the approval of Parliament. Yet Labour MP's have demands for a Brexit agreement that "look designed to be unpassable". Meanwhile, Tory MP's view May's agreement as too soft. Oe possible solution would be to hold another national referendum on Brexit, now that there is a detailed plan for it on the table. As the graphic shows, the type of vote held could result in different outcomes.

In a traditional "first past the post" (aka as "plurality voting" or single-choice) between three options: a hard Brexit, a soft Brexit, or Remain - Remain gets a majority of the votes. But if you use an alternative voting system (aka "ranked choice") where voters rank their preferences from best to worst, a hard Brexit would win. Finally, there is the Condorcet Method where all possible options are matched up head-to-head and the option that wins the majority of the head-to-heads becomes the winner. In this scenario, the head-to-heads are" soft versus remain, hard versus remain and soft versus hard. In the Condorcet form, a Soft Brexit wins two of the three possible matchups.

Note how allowing for a third option - the soft Brexit - allows for ranked choice and Condorcet. Those forms of voting would not be possible with just two options - Brexit or Remain.