Silent Majority & Silent Minority

Basic types of responses

In questions which can be answered "Yes", "No" or "Don't know", two situations commonly arise:

Silent Minority

"Don't know" is assessed as being less likely than each of the other two, with there being no prior reason for selecting one of them as being more likely than the other. This often happens with questionnaires.

Silent Majority

"Don't know" is assessed as being more likely than each of the other two, with there being no prior reason for selecting one of them as being more likely than the other. This often happens with elections, where the majority of the electorate express no opinion.

Silent Minority

To analyse Silent Minority questions, use the step-down underlying set SD(2,3), with "3" representing "Don't know", and "1" and "2" representing "Yes" and "No" in either order.

Since L_SD(2,3)(3)=L_R(3)(3)=1/3²=1/9=0.11, we have:

• Likeliness of "Don't know"= 11%;
• Likeliness of "Yes"=Likeliness of "No"= 44.5%

This histogram shows the likelineses, ie. the average values of Pr(1|f), Pr(2|f) and Pr(3|f).

To see how the values of "Yes", "No" and "Don't Know" vary, Great Likelinesses calculates their CDFs as the following [that for "No" is identical to that for "Yes"]. The red lines identify the median.

In both cases, the median is less than the likeliness, ie the median is less than the mean. This is because of skew, as shown below.

Silent Majority

To analyse Silent Majority questions, use the step-up underlying set SU(2,3), with "3" representing "Don't know", and "1" and "2" representing "Yes" and "No" in either order.

Since L_SU(2,3)(3)=L_SD(1,3)(1)=L_R(3)(1)=0.61, we have:

• Likeliness of "Don't know"= 61%;
• Likeliness of "Yes"=Likeliness of "No"= 19.5%