Cummings writes in What Did the Three-Fifths Compromise Actually Do? Tropics of Meta 04/17/2015 that while the compromise was for counting 3/5 of slaves for purposes of taxation in exchange for counting them also for Congressional Representation, even though slaves actually had zero votes. IN practice, it was rarely used for tax purposes. But it famously gave the slave states, or the Slavepower as its opponents came to call it, extra representation in Congress that was rightly understood in the free states as a slavery bonus in representation:
What Americans got ... is a system of taxation and representation that still bears the impact of the weird compromises that were necessary to accommodate people who owned people. If the tax burden rarely fell on the basis of three-fifths, political power certainly did. The South was able to pad its margin in the House and the Electoral College throughout the first half of the nineteenth century, making possible the many odious compromises and workarounds that sustained slavery. As Einhorn notes, even as the population of the free North swelled due to immigration, Southerners could play the game of balancing power in the Senate through the selective admission of new free and slave states—until the game was up in 1860.He also makes a point that may seem nit-picking at first. But the phrase "all other Persons" was specifically set off from "free persons" in the Constitution. The three-fifths clause did not apply to free blacks, only to slaves. Since most people of African descent in America were slaves in 1787, it is an indication of the extent to which the White Gaze in 1787 did not regard people of color as equal to whites. That attitude would intensify greatly in the following decades. But the clause specifically did not apply to "free persons."
In a final irony, it turns out that the three-fifths compromise actually constrained the full political force of the South in a sense. Prior to the Civil War, the provision meant that Southern states did not get the benefit of counting their entire populations for political representation; afterward, they got 100% representation with the abolition of slavery. As the South gradually disenfranchised black men in the late nineteenth century, their numbers counted for purposes of representation, but not for voting—meaning that the political power of white conservatives was more potent and concentrated than it had ever been before.
The three-fifths compromise was, in the end, just one of many jury-rigged features of American democracy that were meant to constrain it. It was designed to tie the hands of majorities and preemptively constrain the taxing power of the [national] state — a legacy of both the anti-tax spirit of the Revolution and the anti-equality conviction of slaveholders. If its implications for allocating taxes have been far less important than the founders imagined or feared, its impact in terms of amplifying the voice of Southern reactionaries and their descendants has been far more significant. It also reveals one root (among many) of a long-standing American aversion to reckoning with how to tax property and income fairly, since, from the very beginning, a democracy had to account for human beings as both people and property. [my emphasis]
Cummings cites an article by Barbara Jeanne Fields on this point, Slavery, Race and Ideology in the United States of America New Left Review May-June 1990. She argues:
Loose thinking on these matters leads to careless language, which in turn promotes misinformation. A widely used textbook of American history, written by very distinguished historians, summarizes the three-fifths clause of the United States Constitution (article 1, section 2) thus: ‘For both direct taxes and representation, five blacks were to be counted as equivalent to three whites.’ The three-fifths clause does not distinguish between blacks and whites—not even, using more polite terms, between black and white people. (Indeed, the terms black and white—or, for that matter, Negro and Caucasian—do not appear anywhere in the Constitution, as is not surprising in a legal document in which slang of that kind would be hopelessly imprecise.) The three-fifths clause distinguishes between free Persons—who might be of European or African descent—and other Persons, a euphemism for slaves. The issue at stake was whether slaveowning citizens would hold an advantage over non-slaveowning citizens; more precisely, whether slaves would be counted in total population for the purpose of apportioning representation in Congress—an advantage for slave-holders in states with large numbers of slaves—and of assessing responsibility for direct taxes—a disadvantage. The Constitution answered by saying yes, but at a ratio of three-fifths, rather than the five-fifths that slaveholders would have preferred for representation or the zero-fifths they would have preferred for taxation. When well-meaning people affirm, for rhetorical effect, that the Constitution declared Afro-Americans to be only three-fifths human, they commit an error for which American historians themselves must accept the blame. [italics in original]Fields was making a point incidental to a larger argument about what she viewed as misplaced or misleading uses of race as a category in historical explanations. Whether or not one agrees with her larger academic and methodological point, her description of the three-fifths clause is accurate.