The ‘first past the post’ system
Today, social choice theorists and mathematicians who study elections call this the approval voting system followed by a random choice.
As a means of electing candidates, this process fails to reflect the will of the people.
The first-past-the-post (FPTP) system followed in India, the U.S., the U.K., and several other countries has many drawbacks.
Critics have pointed out the disproportionate difference between the popular vote share and the seat share in many Parliaments.
For example, in the 2015 Delhi Assembly elections, the Aam Aadmi Party received 54% of the popular vote but won 96% of the seats, whereas the Bharatiya Janata Party won 32% and 4%, respectively
Second, winners in the FPTP system often secure far less than 50% of the vote share.
No government in India, irrespective of its strength in the Lok Sabha (i.e. number of seats), has ever surpassed 50% vote share.
Since 1918, only once, in 1931 in the U.K., did a government command more than 50%.
So by the vote-share metric India and the U.K. were always ruled by “minority” governments.
Expectedly, social choice theorists disfavour the FPTP system, though it continues to find wide use for its simplicity.
Condorcet and Borda systems
Mathematical analysis to design better electoral systems dates back to the 13th century in the works of Ramon Llull, a missionary and theologian.
His book De Arte Eleccionis, in the Catalan language, gives a detailed algorithm for a two-stage election process for church officials.
It ensures that the winner, when pitted against each of the other contenders, receives more than 50% votes and is the most preferred candidate.
Today, Llull’s method is called the Condorcet system after the 18th-century French mathematician Nicolas de Condorcet, who rediscovered it in the 1780s.
While better than FPTP, the Condorcet system can be difficult to understand and isn’t used in any national election, not least because its mechanism allows participants to prevent the election of a particular candidate.
Some smaller organisations use it to elect their leaders and board members, however.
The Borda electoral process, proposed by French mathematician Jean-Charles de Borda in 1784 — but first described by the 15th-century German astronomer Nicolas of Cusa — is a rank-based voting system (RVS) similar to the points table in sporting tournaments like the Indian Premier League.
It allows voters to rank each candidate on the ballot paper, and through a process of vote redistribution, the winner is guaranteed to have at least 50% of the vote.
Redistribution of votes can take several forms; the most common is to add the second and even third preference votes until one of the candidates crosses 50% vote share.
Like Condorcet, the original Borda method is complex and challenging to implement in large elections such as those in India.
Rank-based Voting System (RVS)
The President of India is elected with the RVS system.
In 1969, none of the 15 presidential candidates secured 50% of the first-preference votes.
After adding second preference votes, V.V. Giri (who had 48% first preference votes) reached 50.8% and was declared the winner, defeating Neelam Sanjeeva Reddy
In 1951, the American economist and Nobel laureate Kenneth Arrow proved that RVS can conflict with certain fairness criteria required of elections.
This doesn’t imply such systems are unfair, even if occasionally the most popular candidate may fail to get elected.
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