The use of different happiness rating scales: Bias and comparison problem?

This paper uses data of reported happiness which is measured at 4, 5, 7 and 11 likert-scale points. A group of 137 respondents was selected to study the comparison problem on the estimated mean happiness using direct rescaling. It is found that the 11-point scale's estimated mean happiness is significantly higher than the 4 and 7-point scale. This paper also proposes an alternate method of rescaling using transition probabilities as weights. This adjusted rescaling resembles the calculation of expected value and provides better mean comparison.