WI: Electoral College uses Borda count

The Borda Count is an election-method where voters rank their preferences, with more points being allotted to more highly ranked candidates. It was developed in France by Jean-Charles de Borda in 1770 and used by the French Academy of Sciences. Let's say that Benjamin Franklin, while he is in France, visits the French Academy of Sciences and is enchanted by this novel form of voting, seeing it as an ideal way to reach consensus in elections and decision-making.
In 1787, he proposes to the Constitutional Convention that the Electoral College give each Elector a first-place vote (worth two points) and a second-place vote (worth one point) instead of two equally-weighted votes. Other than this change, the Constitution is identical to OTL's.
I don't think this would have any effect on the elections of 1789, 1792, or 1796, especially given that candidates did not run as president/vice-president ticket in those races. It would avoid the Jefferson-Burr tie in 1800 that threw the election into the House. Instead, Jefferson and Adams would likely trade places, with Jefferson going from VP to President and Adams being elected to a third term as VPOTUS.
How would this affect future elections? Would parties even bother to run candidates for the vice presidency, since the presidential nominee from the opposite party would almost always finish in second place? Would parties try to cooperate more? Would there be any form of a 12th amendment, either to change the voting system or possibly to increase the influence of the vice president?
 
The Borda Count is an election-method where voters rank their preferences, with more points being allotted to more highly ranked candidates. It was developed in France by Jean-Charles de Borda in 1770 and used by the French Academy of Sciences. Let's say that Benjamin Franklin, while he is in France, visits the French Academy of Sciences and is enchanted by this novel form of voting, seeing it as an ideal way to reach consensus in elections and decision-making.
In 1787, he proposes to the Constitutional Convention that the Electoral College give each Elector a first-place vote (worth two points) and a second-place vote (worth one point) instead of two equally-weighted votes. Other than this change, the Constitution is identical to OTL's.
I don't think this would have any effect on the elections of 1789, 1792, or 1796, especially given that candidates did not run as president/vice-president ticket in those races. It would avoid the Jefferson-Burr tie in 1800 that threw the election into the House. Instead, Jefferson and Adams would likely trade places, with Jefferson going from VP to President and Adams being elected to a third term as VPOTUS.
How would this affect future elections? Would parties even bother to run candidates for the vice presidency, since the presidential nominee from the opposite party would almost always finish in second place? Would parties try to cooperate more? Would there be any form of a 12th amendment, either to change the voting system or possibly to increase the influence of the vice president?

I think, like OTL, there would eventually be an amendment that had the President and Vice President elected jointly. There was a reason why it was done.
 
This makes the situation where the president and vice-president come from opposite parties even more likely. OTL, the Jefferson-Burr debacle could have been avoided by just one Democrat-Republican elector casting one of his votes for Jefferson and not-Burr, and everything happens smoothly. The failure to do just that was a collective action problem. ITTL, you can't do that (barring a massive landslide), as the runner-up will almost certainly be the opposing presidential candidate. The obvious problem means we might very well get the separate POTUS/VPOTUS votes as an amendment even before 1800 (since neither Adams nor Jefferson is going to want a continuation of that situation after the upcoming election, and both will see the party system as being entrenched by that point).
 
How many citizen votes were there? Iirc in the first election most Electors were appointed by the State Legislatures.
Actually, that is technically true, even today. It's just that the States pick electors based on the nominal presidential vote. I say 'nominal', because there is no Constitutional basis for such a vote.

Technically, according to the Constitution, states determine how to choose their electors, and technically it would be legal for a state to appoint a committee of all the left-handed dog catchers in the state to pick their electors.... No doubt the Supreme Court would rule against them, somehow, since they like to 'extend' the plain words of the document, but the those words would allow it.

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PS I'm liberal strict-constructionist. Yep, I might be the only one in the world, but ....
 
That right has been modified in various ways by the 15th, 19th, 24th and 26th Amendments, but afaics these only apply to cases where Electors are chosen by a popular vote. There is no Amendment forbidding the right to vote from being denied or abridged on account of not being a member of the State Legislature, or indeed on account of not being a left-handed dog-catcher.
 
I think, like OTL, there would eventually be an amendment that had the President and Vice President elected jointly. There was a reason why it was done.
Hmmm, what if someone found a way to exploit it first? Maybe Aaron Burr tries to garner Federalist and Jeffersonian support for the vice-presidency in 1796, when the parties don't yet officially back "tickets," and he gets enough support from both factions to edge out Jefferson for VP. Maybe Hamilton would back him behind the scenes if things haven't gotten too strained between them, reasoning that it's better to have a VP who owes you something than a President and a VP who can't stand you (Adams and Jefferson).
 
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