The reason the allowance paid to Senators should be based on population is that the job of a Senator is to represent his constituent.
The function of a United States Senator is many; representing their constituents is one of them.
To represent the constituent effectively, a Senator is expected to speak with the people from his states, discussing and engaging them periodically.
This often requires meeting people in different districts in his state, holding press conferences, town hall meetings, or going to the media.
Each district is based on population, and the higher the population, the higher number of districts or communities a Senator would have to meet and engage.
Hence, in this case, it is concluded that giving senators allowances based on population is justified.
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