Answer by Tiuri for Inequalities, vertical spacing math

This is a rather unusual way of writing an equation. The amsmath package provides a number of environments that is specifically designed to organize multi-line equations. In this case, the gather environment can be an option for you.

Here, I organized your first equation with gather:

\documentclass{scrartcl}\usepackage[utf8]{inputenc}\usepackage[onehalfspacing]{setspace}\usepackage{amsmath}\begin{document}\small\begin{gather*}    (1-p_{i}^{r})(1-p_{o}^{r})2 u(e_{o})+(p_{i}^{r} (1-p_{o}^{r}) + (1-p_{i}^{r})p_{o}^{r} )(2u(\tfrac{e_{i}+\Delta e_{i}+e_{o}}{2})-d)+p_{i}^{r}p_{o}^{r}2 (u(e_{i}+\Delta e_{i})-d) \\    \geq \\    (1-p_{i}^{n} )(1-p_{o}^{n} )2 u(e_{o})+(p_{i}^{n}  (1-p_{o}^{n} ) + (1-p_{i}^{n} )p_{o}^{r} )(2u(\tfrac{e_{i}+e_{o}}{2})-d)+p_{i}^{n} p_{o}^{n} 2 (u(e_{i})-d)\end{gather*}\end{document}

Some notes:

• I replaced \frac with \tfrac to have the same appearance as in your original example. You may want to use \frac again but that will require some adjustments with the braces.
• I used \small to have the full equation fit in one line (so that you see that gather actually centers the equations). Instead of a smaller font size you might add an additional line break or change the page margins. There are also other math environments you can use for very long equations.