Pete Peterson's right! Slaveowners did in effect get "extra votes", as I had put it, in the US House of Representatives and also in the Electoral College because of that system of apportionment, but the slaveholder himself didn't get to cast his ballot multiple times on Election Day.

I took another look at the Wikipedia page about the Three-Fifths Compromise and found this interesting:

EFFECTS -- The three-fifths compromise proved the margin of victory for a number of Southern political successes. Most famously, Thomas Jefferson was dubbed the "Negro President", as his election was dependent on white Southerners benefitting from the partial enumeration of slaves. Also, via Andrew Jackson, the Trail of Tears would never have happened, nor would the ban on congress to discuss slavery have been put into effect. Also, the 1820 Missouri Compromise would never have come into effect. While it is arguable that the 3/5ths compromise may have slowed the day that America came to blows with itself, via the Civil War, it is also arguable that the 3/5ths compromise caused most of the problems between the North and South.

In the 62 years between George Washington and the Compromise of 1850, slave holders held the presidency with the exceptions of John Adams and John Quincy Adams. They ruled all three branches of the government, via appointing southern judges, and having a majority in the senate or the congress or both.

...so, it would seem, the South exercised a form of "tyranny" (though I imagine that Southerners would have been loathe to call it that) over the US government for most of its antebellum existence, thanks to the apportionment of US Representatives! But what about the apportionment of tax revenue? Did the Three-Fifths Compromise mean that tax dollars collected in the industrial North flowed South? Or were taxes collected, as well as distributed, according to the 3/5th head-count?