The principle of the Bicameral Mixedmember Proportional (BMP) Parliament is that the Senate seats be assigned in such a way as to bring the overall proportionality of both houses closer to the popular vote for each province or territory.
The tables below show how it would work for Manitoba. The same methodology would be applied to each province and territory (see Appendix A).
Table 1: StepbyStep to a BMP Parliament for Manitoba
StepbyStep to a BMP Parliament  Example 
For each province or territory, repeat the steps below:  Consider Manitoba in 2015. 
For each party, determine number of seats a party should receive in a BMP Parliament.  Consider the Conservative Party in Manitoba in 2015. 
Specifically, multiple the share of the vote by the combined number of seats in the Commons and the Senate.  The Conservatives received 37.4% of the vote. Manitoba has 14 Commons seats and 6 Senate seats for a total of 20. 37.4% x 20 = 7.48 seats. The Conservatives therefore earned about 7½ seats in Manitoba. 
Determine the number of seats a party should receive in a BMP Senate.  The Conservatives won 5 seats in the Commons. 
Subtract the number of Commons seats won from the number determined above.  The Conservatives should therefore win 2.48 seats in the Senate, representing Manitoba. 
First round: Since fractional seats cannot be awarded, first award any integer seats.  Award 2 BMP Senate seats to the Conservatives in Manitoba. Repeating the exercise for the other parties in Manitoba awards 1 seat to the Liberals and no seats to the other parties, since they each earned less than one whole seat. 
Second round: Determine the awarding of remaining Senate seats.  Manitoba has 6 – 2 – 1 = 3 seats unawarded. 
Specifically, rank the parties in descending order by the fractional seats they should receive. 
For Manitoba, the fractional seats remaining are as follows:

Award the remaining seats to the parties ranked by remainder in descending order.  For Manitoba, the 3 remaining seats would therefore be awarded to the Liberals, NDP and Greens respectively. 
Add the seats awarded in the first and second rounds above to reveal the final Senate composition for the province or territory. 
For Manitoba, the Senate composition would be as follows:

How does this compare to the popular vote? Table 2 compares the BMP Parliament derived above to the popular vote in Manitoba.
Table 2: Comparison of BMP Parliament to the Popular Vote for Manitoba
Party  Popular Vote  House of Commons  BMP Senate  Overall BMP Parliament 

Fraction  Seats  Fraction  Seats  Fraction  Seats  Fraction  
CPC  37.4%  5  35.7%  2  33.3%  7  35.0% 
LPC  44.7%  7  50.0%  2  33.3%  9  45.0% 
NDP  13.6%  2  14.3%  1  16.7%  3  15.0% 
GPC  3.2%  0  0.0%  1  16.7%  1  5.0% 
Other  1.1%  0  0.0%  0  0.0%  0  0.0% 
Total  100.0%  14  100.0%  6  100.0%  20  100.0% 
Overview  Appendix A  Appendix B  Appendix C  Appendix D 