**Edited, I found some answers in the Help documents***
I've looked through the documentation for ArcGIS Cell Statistics (Spatial Analyst -> Local -> Cell Statistics) and it appears that it assigns NoData for ties. Is there a way to change this? For example, say I have several classified rasters and I'd like to run a majority vote on each pixel to see which class is the majority for each pixel based on these multiple maps and in the case of a tie I want MapX's value to be assigned to the pixel.