How is the size of a video related to its perceived quality? Video is often presented at different sizes. On the Internet, many websites provide quite a few size settings. In the store, you can buy TVs of many different sizes. In both cases, it's the same resolution video being stretched to a various sizes. To the technically savvy, making the same pixel occupy a larger physical space does not increase the quality of the video. But to the average consumer, he may think bigger is better. 

What does the graph of perceived quality VS physical size look like? Is it linear, that is bigger is always better. Or is it parabolic? That is, there is a perfect ratio of pixel to size and any deviation from this ratio will result in a worse perceived quality. Or is it some other shape?
At least for images (I don't know of such a result tested on videos) for a given resolution, there is an optimal display size (assuming constant viewing distance. otherwise, display size should be measured in angles from the viewers point of view). In a paper from 1989, Peter Barten provided a formula to compute this effect [1]. The gist can be seen in the following figure from that paper: 



For the low resolution images (e.g 100px wide) there is a slight advantage in quality ranking for the smaller screen over larger ones. However, as the number of pixels increases, the perceived quality on the small screen saturates, and larger screen are preferred.



[1]  The Effects of Picture Size and Definition on Perceived Image Quality. Barten, P. G. J; IEEE Trans.on Electron Devices, 36 (9), p. 1865-9, Sept.1989
doi: 10.1109/16.34260