by to society

When is a person old? There are many individuals who still seem ‘young’ at seventy or more, while others appear ‘old’ in their fifties. From another point of view, sumô wrestlers, for instance, are ‘old’ in their thirties, whereas artists’ best years may come in their sixties or even later. But in general, people are old when society considers them to be old, that is, when they retire from work at around the age of sixty or sixty-five.

People are normally regarded as old when ( ).
? they are in their fifties
? they are judged to be old by to society
? they consider themselves too old to work
? they reach the age of seventy

The answer is "2".
In this sentence is "to" or "by" necessary?
If so, what role does this play?