Free market elections (for countrys that believe the free market)

Effectively in american elections a person must decide democrat? or
republican? before he or she marks their x. Nobody else has a chance.
The person may prefer the republican that lost the primary, green comunist
socialist or christian or muslem right but if they make that choice they
are effectively negating their vote. So some nuckle down down and vote
pragmatically, many dont vote at all and a few vote with their heart.
The Nader voters in the last presidental election are a good example or ross
perot people before that. They effectively gave the election to their
greatest enemy. 
The real problem is choice. Democracy should not be a simple right left
thing with just 2 partys. In the Ireland (south) system, in an election a
voter has the choice between say 3 republicans, 3 democrats, a green, and
one or 2 from other partys.  And we dont put x beside a particular
candidate. We are educated and can count so we put 1 beside the favorite, 2
beside the second favorite and so forth.  Using a relatively simple
mathematical system, we count out the votes and when a candidate reaches
his quota, he or she is deemed elected. we elect 3 4 or 5 from an
electoratal area. (It should all be 5 seat areas in my opinion)
All counting is by hand (Counting by machine is never allowed) and officials
from the partys and the public are allowed and encouraged to watch(to
assure confidence in the system) Open Competition BETWEEN and WITHIN partys
for the spoils keeps the partys honest.
 You cannot impose a guy that the locals hate in this system. They will just
vote for the other guy. This system
gives great statistical information to the partys so they can change their
polocys to diliver what the electorate want. It is a true free market
system! The consumer has plenty of nuances to choose from both within and
between partys.
Not like the American system where the 2 leading brands are locked in an
unbreaking (and unbreakable) monoply.
I am wondering if it can be tried in the USA or Canada. Would it be legal to
offer people choice here?
Brian White