Why do voters support public schools? The median-voter result allows us to narrow this question to Why

Question:

Why do voters support public schools? The median-voter result allows us to narrow this question to Why does the median voter support public schools? The median voter will vote in favor of public schools if his (or her) benefit exceeds her cost (his or her tax liability). When will that happen?
Table provides an example with three voters with different incomes. In Scenario A voter 3 has a very high income, so the median income ($20) is less than the average income ($30). In this case, the median voter has only 22 percent of total income (20/90), and if school taxes are proportional to income, the median voter will pay only 22 percent of school taxes. If the benefit of education is distributed equally across voters, schooling looks like a good deal to the median voter: Pay 22 percent of taxes to get 33 percent of the benefits.
In Scenario B the median income is greater than the average income. In this case, the highest-income voter doesn€™t earn much more than the median voter, and the median voter has 40 percent of total income (20/51) and thus pays 40 percent of school taxes. Compared to Scenario A, public schooling appears less attractive (pay 40% of taxes to get 33% of benefits) and if the median voter bases her decision strictly on her own benefits, a NO vote is more likely.

A recent paper finds evidence that in the early years of public education (in the 1800s), Scenario B generated strong voter support for public schools. In other words, even when the median voter faced an above-average tax liability, he or she voted in favor of public schools. One interpretation of this result is that the median voter based his or her vote on both the private and the external benefit of education. Suppose the education of others increased the welfare of the median voter by a relatively large amount. In that case, the external benefit experienced by the median voter will be large enough to offset his or her relatively large tax bill, and the rational response is to voteYES.