Ten first-world countries have single-payer:  Norway, Japan, UK, Sweden, Canada, Finland, Italy, Portugal, Spain, and Iceland.  

Seven have a two-tier system: NZ, Netherlands, Denmark, France, Australia, Ireland, and Hong Kong (if you still want to count them).    

An insurance mandate (akin to the US's) is provided in Germany, Belgium, Austria, Luxembourg, South Korea,  Greece (...first-world?) and Switzerland.