This means an election for an elected position, with people directly voting for the choice of candidates (e.g. US Presidential elections don't count, since they are votes for the electors and not directly for the President).
Referendums on a topic also don't count.
The current response to this question is the 2014 Brazil direct presidential election.
(Being precise of what is asked it is its first round, since more votes were casted.
But following a criterion of votes effectively casted to any of the candidates, the answer would be the second round).
See details below: In the first round (October 5) there were 142 822 046 eligible voters of whom 115 122 611 voted ( 104 023 543 effectively in 1 of the 11 candidates, the difference accounting for nulls or blank votes).
In the second round (October 26) there were the same 142 822 046 eligible voters of whom 112 683 879 voted ( 105 542 274 effectively in 1 of the 2 remaining candidates, the difference accounting for nulls or blank votes).
By the way, with this election, Senator Aecio Neves also holds the record as the most directly voted runner-up (losing with a record of 51 041 155 votes).
On the other hand the re-elected President Dilma Roussef, with 54 501 119 just held the title of the second most voted winner on a direct election.
She herself received more votes in the 2010 election ( 55 752 529 ).
Besides that, the Oscar to the most directly voted person on an election goes to Lula da Silva, with 58 295 042 in 2006.
Observation: note that in the second round less eligible voters showed up to the ballot (~112 millions versus ~115 millions 3 weeks sooner), nevertheless the sum of the votes for the remaining two candidates (~105.5 million) exceeds the sum of theirs plus the previous other 9 candidates 3 weeks before (~104 million) with more than 1.5 million votes.
References here .
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The world's largest democracy is India, and as such, it is not unreasonable to assume that this is the world's largest election.
In 2009, for example, the total vote count was 714 million which is larger than that of the United States and EU combined.
In a fashion similar to that of the United States President, the President of India is indirectly elected through electors , but if the President of the United States can be said to be elected "by the people" (and indeed, there are vote tallies that often show how many people "voted for the candidate"), then the same can be said of the President of India.
In 2012 , there were over 700,000 electoral votes (compared to 538 in the United States) cast for Pranab Mukerjee and another 300,000 for his closest rival.
Each of these electors is traceable to the will of 1,000 residents in each state, meaning that over a billion people are represented.
That said, since the question directly excludes electors, we need move on to the Lok Sahba.
In 2009, Manmohan Singh's Congress Party received over 153 million votes in a three-way election that the United Kingdom's Guardian called the "world's largest democratic poll" .
The election itself was 28 days long and involved nearly 700 million voters.
In a party based system, the choice of party could be considered tantamount to choosing its leader, so may or may not fall within the scope of the question.
That all said, with only 543 seats in the Lok, there is bound to be a single constituency within that body that would almost certainly take the prize.
In contrast to China, its logical rival, which has 2,987 members in its parliment and is of dubious democratic value, the sheer number of members (4 times the members, similar sized electorate) dictates that each seat in India would have the most direct electors per position.
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Actually Indonesia has a larger voter population than Brazil (the accepted answer).
For the 2019 election On 5 September 2018, the KPU announced there were 187 million registered voters – 185,732,093 in Indonesia and 2,049,791 voting abroad.
The Indonesian president is directly elected albeit in a two-round system (like Brazil), but candidates need the support of 20% of political parties (as represented in the Indonesian parliament = DPR) for their nomination.
In the aforementioned election, there were 154,257,601 valid votes cast in the presidential contest, substantially more than in Brazil (as an absolute number, the participation rate was pretty similar around 80%).
Although the election was also fairly split 55.5% vs 44.5%.
Jokowi won with 85,607,362 also a larger absolute number than for Brazil's election from the accepted answer.
These numbers also comfortably "beat" the 2018 election of Bolsonaro as well: 147,305,825 registered voters, 117,364,560 votes cast, 57,797,847 votes for Bolsonaro (2nd round).
For the sake of mentioning this too, Brazil is considered somewhat more democratic/freethan Indonesia in both in EIU's democracy index and Freedom House's .
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The correct answer to this question in its current form would be the following.
The largest direct election to a single position by the number ofeligible voters is the 2012 presidential election in Russia.
Therewere 109 860 331 eligible voters of whom 71 104 543 cast a vote.
Therewere 109 860 331 eligible voters of whom 71 104 543 cast a vote.
There were
106 484 518 eligible voters ofwhom 79 471 282 cast a vote.
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2014 Indian parliamentary elections won by Narendra Modi led the Bharatiya Janata Party (BJP) government.
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What was the largest popular vote election ever held for a personally-held position?  This means an election for an elected position, with people directly voting for the choice of candidates (e.g. US Presidential elections don't count, since they are votes for the electors and not directly for the President). Referendums on a topic also don't count.  I'm fine with any reasonable method of measuring the size (# of eligible voters, or # of actual votes cast).
What was the largest popular vote election ever held?
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<election><democracy><voting><voting-systems><one-person-one-vote>
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The 2014 Indian parliamentary elections, won by Narendra Modi, led the Bharatiya Janata Party (BJP) to government. The largest direct election to a single position by the number of eligible voters was the 2012 presidential election in Russia. The answer may be either of: the 2014 Indian parliamentary elections; or the 2012 Russian presidential election.  
The answer may be either of: the 2014 Indian parliamentary elections; or the 2012 Russian presidential election.  