The Physics and Math of keeping elections fair and representative

Context:

Throughout the world, elections representing a complex blend of emotions, hopes, conflicting ideologies, and occasionally, instances of violence have a scientific underpinning.

Ancient Electoral Practices: 

• Ancient Athens: About 2,500 years ago, the earliest form of elections in ancient Athens was a system that depended on the candidate’s luck.  Among all the suitable candidates, one was randomly chosen. 
  • Since the winning criterion was based on random choice, campaigning or influence couldn’t help the candidate.
• Kudavolai’ System by Chola Rulers: Tenth-century Chola inscriptions at Uthiramerur in Tamil Nadu reveal the practice of choosing village representatives through a ‘Kudavolai’ system. 
  • The final choice was made by randomly picking one among the candidates the people had voted for. 

First Past the Post’ System(FPTP):

• About: An electoral system in which voters vote for a single candidate, and the candidate with the most votes wins the election.
  • It is one of the simplest and oldest electoral systems.
• Mechanism: Voters are presented with a list of candidates nominated by different political parties or fighting elections as independents. 
• Voters choose one candidate by marking their ballot paper or electronic voting machine. The candidate who receives the most votes in a constituency is declared the winner.
  • The winner does not need to get a majority of the votes, but only needs the largest number of the votes.
• Approval Voting System: The system followed in India, the U.S., the U.K., and several other countries has been called by the social choice theorists and mathematicians as the approval voting system followed by a random choice. 

Drawbacks of FPTP: 

• Discrepancies Between Popular Vote and Seat Allocation: 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.
• Challenges of Vote Share: Winners 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. 
  • As a means of electing candidates, this process fails to reflect the will of the people. 
  • Since 1918, only once, in 1931 in the U.K., did a government command more than 50%. So, by the vote-share metric, rather than parliamentary seats, India and the U.K. were always ruled by “minority” governments. 

Mathematical Analysis to Design Better Electoral Systems:

• Condorcet Systems:  
  • About: In this, the winning candidate must achieve an absolute majority of the total number of formal votes. This means that the winner of each contest must get more than 50 percent of the total formal votes.
  • Analyzing Voter Preferences through Preference Rankings: In this, voters list candidates based on preference rankings. Subsequently, each candidate is compared against every other candidate in individual pairwise comparisons.
  • Comprehensive Algorithm for a two-stage Election Procedure: It outlines a comprehensive algorithm for a two-stage election procedure. 
    • It guarantees that the winner when competing against each of the other candidates receives more than 50% votes and is the most preferred candidate.
  • Concern Associated: While better than FPTP, the Condorcet system can be difficult to understand and isn’t used in any national election because its mechanism allows participants to prevent the election of a particular candidate.
• Borda Systems:  
  • Rank-based voting system (RVS):  It is a RVS which 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. 
  • Vote Redistribution Strategies: Redistribution of votes can take several forms with the prevalent method involving the accumulation of second and sometimes even third preference votes until a candidate surpasses a 50% vote share.
    • The President of India is elected with the RVS system.
  • Implementation Challenges: Like Condorcet, the original Borda method is complex and challenging to implement in large elections such as those in India.
    • 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. 

How can maths, physics help keep elections fair?

• Unveiling Patterns in Electoral Processes: Analysis of election data has unveiled emerging patterns reflected in the distributions of significant factors within the electoral process. 
  • Although mathematics clarifies the chaotic nature of election processes, physics utilises this disorder to look for general patterns across electoral systems. 
• Resilience of Patterns: Despite the apparent disorder surrounding elections, these patterns exhibit resilience and remain unaffected by finer intricacies such as geographical locations, voting paradigms, or cultural contexts. 
  • Thus, while mathematical analysis refines algorithms for the electoral process, a physics perspective assists in assessing whether these algorithms are equitably implemented in practice. 

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