Here's an interesting chart, pertaining to the year 2000 U.S. elections:

What it says is this:

If, for the eleven states with the most electoral votes, one candidate received a slim majority (of the votes cast for Bush + Gore), namely 2 greater than 50% of the Bush+Gore Total, that candidate would win the 270 electoral votes necessary to become president ... and that would be only 27% of the total (nation-wide) number of votes cast for Bush+Gore!

>Huh? 27%? You're kidding, right?
That got me to thinking of a better way which would give the position of head-of-state to the candidate with the most votes (not just 27%).

Here goes:

• Assume that the total number of people (nation-wide) that can vote is P
      (example: P = 100,000,000 voters in the country)
• We divide the country into N equally populated electoral units each with a prospective government repesentative
      (ex: N = 200 units ... so 200 elected officials - one from each unit)
• Each unit has precisely P/N people that can vote
      (ex: P/N = 500,000 voters per unit. They elect the local government representative.)
• The party with the greatest number of elected officials forms the new government.
• Assume that, in precisely half of the N units (ex: that's N/2 = 100 units), Sally's party receives 1 greater than 50% of these P/N votes.
  Then Sally receives (1/2)(P/N) + 1 votes for her party.
      (ex: 250,001 votes in each of N/2 = 100 units)
• This slim majority gives Sally's party the government representative from that unit.
  This plurality in half the electoral units then gives Sally half of the N representatives, namely N/2
      (ex: N/2 = elected 100 reps)
• The total number of votes received by Sally in the N/2 electoral units (where she won by the slim majority) is
  (Number of Units)(Votes per Unit) = (N/2){(1/2)(P/N)+1} = P/4 + N/2
      ex: (100 units)(250,001 votes/unit) = 25,000,100 votes
• To get the percentage of the total available votes (total votes = P) we divide by P and get 1/4 + N/2P.
      ex: (25,000,100)/(100,000,000) = .250001 or 25.0001%

>Who's Sally?
She's the leader of the party. If her party wins more reps than any other party, she becomes head of state.

In general, since N is usually small compared to P - the elected representives are a small fraction of the voting populace - then N/2P is small compared to 1/4, so we conclude (surprise!) that one candidate can win half of the representives with little more than 1/4 or 25% of the popular votes.

>Picture? Yeah, maybe a picture is worth ... uh, a thousand votes. >That's your "better" system? Uh ...