Which preposition to use with eligibility

to Occurrences 10%

This was also the age for eligibility to the Roman Senate.

of Occurrences 5%

Their circles are to an extent exclusive, because some distinction must mark the eligibility of members.

for Occurrences 3%

There was no question as to my eligibility for service.

in Occurrences 2%

some cases canvass valves are used for pumps, with the effect of materially mitigating the shock; but they require frequent renewal, and are of inferior eligibility in their action to the slide valve, which might in many cases be applied to pumps without inconvenience.

Which preposition to use with  eligibility