Well since you DV is party I would use multinomial logistic regression. See the link: https://www.bing.com/search?q=multinomial+logistic+regression&qs=SC&pq=mutinomial+logistic&sc=8-19&cvid=FCF26A3C39304C4B8532B47B0CAC6DDA&FORM=QBLH&sp=1

BTW, I assumed that you were considering no. of parties>2. If limiting yourself to the 2 major parties use binary logistic regression.

To do this in your favorite package, add the package name to the query

Best, David Booth

If you consider your DV coded as a continuous variable you can read the % each IV contribute to the variance in your DV by reading the part correlation for each significant IV and then square it, Then you have the % for each IV:s contribution to the variance in DV

If you DV is not a continuous variable follow Dr Booth's advice.

Thank you David and Beatrice for your advices! This will be of great use to me

After doing all the analyses, in the final multinomial logistic regression this pops up:

There are 73.5% cells (i.e., dependent variable levels by subpopulations) with zero frequencies.

Could you please explain me in plain language what this means? The sample is not representative enough to make the final arguments?

Many Thanks

multinomial logistic regression would be useful