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That may have been true in the past but it may not be true today.
From the Cambridge study in the link it shows the voting trends by income percentile from the 1980s on. The trend has been for more affluent people to vote democrat. The Democratic Party has become the party of extremes for low and high income voters, with a diminished middle-income voter representation. The gist of the study is, how is the Democratic party with it's growing base of affluent, liberal voters promote its traditional policies favoring redistribution of wealth without impacting these same, affluent voters? The low income voters want whatever gimmees they can get because they don't have to pay for them. The rich and affluent who might be impacted by higher taxes want social programs that benefit them somehow, such as investment in education spending. Although it isn't stated it looks to me like the middle class ends up getting screwed with higher taxes and not seeing any of the 'free stuff'.