I was going to sign the petition, but thought I'd find out the details and, I'm sorry to say, I'm not going to sign.
The government needs to get a grip of the housing situation, but keeping pensioners in under-occupied social housing is not the way.
I looked up the details for my own district.
47.8% of social housing is under-occupied. About half of the under-occupiers have one spare bedroom. The other half have two or more spare bedrooms.
Of the under-occupiers, 35% are pensioners (singles or couples) and 39% are 'empty nesters' (working age people with no children at home).
Not all of the above are in receipt of housing benefit, but some are. In some cases, pensioners will be receiving housing benefit to live in three or bedroom houses. They are also exempt from paying Council Tax.
Meanwhile, there are over 1,000 people (mainly families) on the council housing list. Nearly a half of families are living in inadequate housing, ie they don't have enough bedrooms.
Tenants in private accommodation are restricted in the amount of housing benefit they receive and, in this area, the LHA rate is way below the actual rents, so they are already paying towards rents out of benefits, if they claim them.
My area isn't the worst, although some areas, especially big towns and cities, which have different problems, have less under-occupation.
The need for new social and affordable housing could be reduced considerably, if under-occupiers could be persuaded to move. Of course, this means investing in suitable one bedroom, ground floor housing (bungalows). Private developers won't do it, because they can't make a profit, so the government (via councils) has to take the initiative. I would happily sign anything to support the building of more housing suitable for pensioners.