Attached is a link to a web site and video that has the potential to solve both your potato and hosta problems. Best of all, it is an organic solution. Using a watering can, put in 1 teaspoon of castor oil and 1 teaspoon of dishwashing detergent and then fill it with water. Spray it over the ground to be protected. Simple enough if you only have a small area. There is a bit more detail on the web site but those are the basics.
http://www.nhhostas.com/organic-vole-control.htm
I have had problems in the past with my beets being eaten by a vole and they looked very similar to your potatoes (half eaten). I tried this treatment for the first time this year and it appears to work.
Unfortunately, I did not treat the ground right beside it for my snow peas and the vole has moved on to them. At least I will know for next year.