If the margin or error is 3% then its a tie across a 6% range.
Not quite. The "confidence level," which is rarely disclosed with the poll results, is as important, if not more important, that the margin of error. For example, if the confidence level is 95% and there is a 3% margin or error, then there is a 95% chance that the polled results are within 3% of the actual results, and a 5% chance that the polled results are greater than 3% (plus or minus) of the actual results.