that depends on, when the confidence interval was very wide, the 95% and 50% will be very close to each other and reporting 50% would lend more precise to the effect size under investigation. If the confidence interval is wide, using 50% may cause confusion. after all, there is 50% possibility that the true effect will locate outside the interval, this is not very confident.

I don't have any strong opinions about this (yet), but I recently read this over at Andrew Gelman's blog:

"I prefer 50% to 95% intervals for 3 reasons:

http://andrewgelman.com/2016/11/05/why-i-prefer-50-to-95-intervals/

A curious point of view. Why is 50% more intuitive than 95%? And what do we learn from an interval that is as likely to be wrong as right? In health sciences, it's useful to have some idea of what is unlikely.

I don't understand the first point: at least for usual CI, it only change the quantile to use, and I don't see why 0.25 quantiles would be computationally more stable than the 0.025 ones.

I'm not convinced by the second one, I don't see why "95 % of the interval" is less intuitive than "half" or at least "three quarters".

I don't really the third point either, for that a ponctual estimate is enough...

After saying that, I agree that 95% is purely conventional and that in theory, any confidence level can be used as far as it is stated, and it can be adapted to the situation. Even if being wrong half the time seems at first glance not very trustworthy... In principle, no problem.

I note that Andrew in his blog was trying to model statewide election results.  FiveThirtyEight in their modelling of US elections presented 80%CIs.  In what I do in medicine, larger CIs (95% or 99%) are more appropriate, usually from a safety or resource utility perspective.

As an aside - some of interpretations of CIs are not quite right. I found a recent publication very helpful in understanding this: 

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/ 

Thank you very much for your contributions. I really appreciate all of them.