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Percentages are often very deceiving when we don't focus on the denominator. Perhaps the most famous deception is the claim that "The top 1% of taxpayers pay 40% of the income taxes." This is a spin intended to cause the listener to make a mental comparison between the "1%" and the "40%" ... as though it's "one apple" vs. "forty apples." It is intentionally deceptive. If, for example, that same "1%" collected 50% of the income, we should easily conclude that they are unfairly under-taxed and grossly overpaid. That's a conclusion that's the opposite of the impression intended. That's why it's propagandistic -- as most half-truths are.
So, how does that apply to the chart? In a specific county, if the number of registered Republicans increases by 10% and the number of registered Democrats increases by 5% we cannot know the actual number of people those increases represent without knowing how many there were to begin with.
In Denver County, for example, the number of Republicans decreased by 11.6% and Democrats decreased by 8.0%. But the number of Democrats in that county is twice as large as the number of Republicans (45.1% v. 22.4%) so, in the actual number of people, the Democrats lost more voters, albeit at a lower rate.
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