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It should be able to handle 10 questions, each with multiple choices, and to display the results in real time on a world map, using colors. Geo-location of each respondent is detected in real time based on IP address. The color displayed (for each respondent) would represent the answer to a question: for instance male = red, female = yellow, other = green. I used to work with Vizu: the poll service was available as a web widget, offering all these features for free, but it's now gone. It would be great if it can handle 2,000 actual responses, and if you can zoom in on the map.

Any recommendation? Either a free or paid service.

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Answer by Andrew Goodchild:

If you are willing to cut some code, you could plug shiny and survey monkey together. 
Survey monkey have a new rest api: https://developer.surveymonkey.com 

If you don't want to cut code, the simplest solution is to probably look at google survey: 
http://www.google.com/insights/consumersurveys/home 

Although to be honest an R library for survey monkey would be far cooler.

This map might look nice when there are a dozen of results but will look very busy when the number goes above 100. Also, Keep in mind the spatial disparity between cities and rural areas so a country level display may not be that effective. Just a suggestion from an experienced cartographer.

I can do it by programming a dedicated program but the zoom part will be more difficult.

You can program the form or use a tool for it like limesurvey or formidable on top of wordpress.

For displaying and show the data you have to program.

There are same tools that show where your visitors are from in a map similar to that but usually show all as red. Maybe it is possible to adapt such a tool.

I will be interested as well in know if you are able to solve this somehow.

What is the use of displaying result of polls in real time? Won't it be useful to display the results when all the data has been collected and then display it on map.

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