Bi-wire v's single with jumper leads.

There's a very sound reason why bi-wiring works.

Remember that your crossover is basically a filter that splits the signal inside your speaker and sends the highs to the tweeter and the lows to the woofer. Up until that point, all frequencies travel together along the single speaker cable.

By removing the jumpers and using bi-wired cables, the high and low pass filters become part of each loop right back to your amp terminals, meaning that the high frequencies can't travel along the woofer cables and vice versa. This helps to reduce distortion and smearing of the sound. It's very similar to the way S-video cables separate the luminance and chrominance signals to improve picture quality over composite cables.

But as Shadorne said, if your speakers/system isn't truly suited to bi-wiring, you may hear little or no difference.
At the very least, you've doubled your wire gauge!

While the back emf from the LF driver does create a signal that beats with the higher frequency components to produce distortion in the range of the HF circuit, I question the extent of that signal. Thevenizing the respective circuits (with a signal sources from the amp and signal source from the LF driver) results in a large disparity in loads. Unless the output Z of the amp and cable are significant in comparison with the Z of the HF circuit the amount of IMD should be extremely small. Most decent amplifiers and just about any cable at length less than say 20 feet present a Z orders of magnitude less than the HF circuit. While biwiring will affect the IMD caused by the LF driver signal, it is unlikely that the IMD thus generated is of any practical signficance in most instances.

Jams70: Put all the analysis aside and simply listen for YOURSELF.

I think biwiring works if you can filter the HF and LF before the speaker cables, or even before your power amp.

The ideal would be according to me:

LF-power amp- speaker cable-tweeter
pre amp <
HF-power amp- speaker cable-woofer

This being 1 channel, if you have 3 way or more then repeat for each.
I don't understand why some 3 way speakers have bi-wire option shouldn't they have a tri-wire set up.

Bi wiring will not always give you a better sound. It really depends on the speakers and it's cross over design.
If you really want to go the bi wiring route then you need to go what I call true bi wiring meaning 4 seperate runs to each speaker. The 2-4 design is a bit waste of time and might as well use single wired with jumpers instead.
Hope this helps.