I am building an ASP.Internet MVC site where I wish to use OpenSTV to conduct polls. To operate results through OpenSTV, I'd need to run the executable. Is the fact that permitted from the medium-trust ASP.Internet application?

You cannot instantiate a System.Diagnostics.Process object unless of course you are running at FullTrust.

Should you examine the characteristics designing the category you will see the interest in FullTrust:

Process Class (MSDN)

[PermissionSetAttribute(SecurityAction.InheritanceDemand, Title = "FullTrust")]

[HostProtectionAttribute(SecurityAction.LinkDemand,

        SharedState = true, Synchronization = true,

    ExternalProcessMgmt = true, SelfAffectingProcessMgmt = true)]

[PermissionSetAttribute(SecurityAction.LinkDemand, Title = "FullTrust")]

public class Process : Component