BTW, my next choice over an Olympus would be a new/old stock Nikon 1 Series, like the early J or S models. The CX sensor is the same size as the Sony RX100 "One-inch" sensor, but from a different fabricator. The early Nikon CX sensors weren't quite as good, but still better than most teensy sensor P&S and smart phone sensors.
I wish I'd bought an early J1 when Nikon was blowing 'em out a few years ago for a little over $100 with the 10-30 kit zoom. Would have made a great knockaround bicycling camera. But I wasn't bad in the saddle then and hadn't anticipated the need for a good compact and rugged camera.